This method makes it extremely easy to back up my entire photo collection by dragging the "Pictures" folder to a different drive. It also makes it easy to reference and review the photos in rough chronological order. This is why I've never understood the purpose of third-party "photo management" software, since most such software inevitably reorganizes the underlying directories in its own crazy way, or builds a proprietary index of photos that takes the user away from the actual directory structure. If you're aware of the organization of your photos on your disk, then any additional management software becomes superfluous.

At any rate, there is one slight issue with this style of organizing photos: all of the various sources of photos (different cameras, scanners, cell phones, etc) give different file names to the photos! So, when all the photos are combined into a single directory, they often conflict with each other, or at the very least become a disjointed mess. For example, the file names can be in the form DSC_xxxx, IMG_xxxx, or something similar, which isn't very meaningful. Photos taken will cell phones are a little better; they're usually composed of the date and time the photo was taken, but the naming format is still not uniform across all cell phone manufacturers.

Thus, the optimal naming scheme for photos would be based on the date/time, but in a way that is common between all sources of photos. This would organize the photos in natural chronological order. The vast majority of cameras and cell phones encode the date and time into the EXIF block of each photo. If only there was a utility that would read each photo, and rename it based on the date/time stored within it. Well, now there is (download it)!

This is a very minimal utility that takes a folder full of photos and renames each one based on its date/time EXIF tag. As long as you set the time on your camera(s) correctly, this will ensure that all your photos will be named in a natural and uniform way.

The tool lets you select the "pattern" of the date and time that you'd like to apply as the file name. The default pattern will give you file names similar to "20111028201345.jpg" (for a photo taken on Oct 28 2011, 20:13:45), which means that you'll be able to sort the photos chronologically just by sorting them by name!

It has always baffled me why we define π to be the ratio of the circumference of a circle to its diameter, when it should clearly be the ratio of the circumference to its radius. This would make π become the constant 6.2831853..., or 2 times the current definition of π.

Why should we do this? And what effect would this have?

Well, for starters, this would remove an unnecessary factor of 2 from a vast number of equations in modern physics and engineering.

Most importantly, however, this would greatly improve the intuitive significance of π for students of math and physics. π is supposed to be the “circle constant,” a constant that embodies a very deep relationship between angles, radii, arc lengths, and periodic functions.

The definition of a circle is the set of points in a plane that are a certain distance (the radius) from the center. The circumference of the circle is the arc length that these points trace out. The circle constant, therefore, should be the ratio of the circumference to the radius.

To avoid confusion, we’ll use the symbol tau (τ) to be our new circle constant (as advocated by Michael Hartl, from the Greek τόρνος, meaning “turn”), and make it equal to 6.283..., or 2π.

In high school trigonometry class, students are required to make the painful transition from degrees to radians. And what’s the definition of a radian? It’s the ratio of the length of an arc (a partial circumference) to its radius! Our intuition should tell us that the ratio of a full circumference to the radius should be the circle constant.

Instead, students are taught that a full rotation is 2π radians, and that the sine and cosine functions have a period of 2π. This is intuitively clunky and fails to illustrate the true beauty of the circle constant that π is supposed to be. This is surely part of the reason that so many students fail to grasp these relationships and end up hating mathematics. A full rotation should be τ radians! The period of the sine and cosine functions should be τ!

But... wouldn’t we have to rewrite all of our textbooks and scientific papers that make use of π?

Yes, we would. And, in doing so, we would make them much easier to understand! You can read the Tau Manifesto website to see examples of the beautiful simplifications that τ would bring to mathematics, so I won’t repeat them here. You can also read the original opinion piece by Bob Palais that explores this subject.

It’s not particularly surprising that the ancient Greeks used the diameter of a circle (instead of the radius) in their definition of π, since the diameter is easier to measure, and also because they couldn’t have foreseen the ubiquity of this constant in virtually all sciences.

However, it’s a little unfortunate that someone like Euler, Leibniz, or Bernoulli didn’t pave the way for redefining π to be 6.283..., thus missing the opportunity to simplify mathematics for generations to come.

Aside from all the aesthetic improvements this would bring, considering how vitally important it is for more of our high school students (and beyond) to understand and appreciate mathematics, we need all the “optimizations” we can get to make mathematics more palatable for them. This surely has to be an optimization to consider seriously!

From now on, I'm a firm believer in tauism! Are you?

Before we go on, let’s calm down a bit. Even if these results are somehow confirmed, it wouldn’t “prove Einstein wrong,” or cause scientists to stop using General and Special Relativity on a day-to-day basis. If anything, it would show that Einstein’s theory is incomplete, but no one is disputing this in the first place.

Relativity (general and special) has been put through dozens of independent, precise, elaborate tests, and passed every single one with astonishing accuracy, which means that there’s definitely something fundamentally correct about Einstein’s theory. It shouldn’t be thought of as some kind of “sitting duck” theory, just waiting to be overthrown.

Understandably, the current consensus among the world’s physicists seems to be that there was a measurement error in the OPERA experiment, or that the experimenters neglected to integrate some subtle factor that accounts for the missing 60 ns. (For a wonderfully accessible introduction to the OPERA experiment, as well as particle physics in general, read Matt Strassler’s blog. For a more thorough discussion of possible mistakes, read Lubos Motl’s post on the subject. It's also worthwhile to read the comments on those blogs.)

Perhaps the most convincing evidence against this experiment is that we have observed neutrino emissions from supernovae (specifically SN 1987A), and these neutrinos more-or-less coincided with our observation of visible light from the same supernova. If neutrinos are really faster than light, we should have observed the neutrinos many months before we observed the light. The only loophole in this argument would be if the OPERA effect is energy dependent, since the OPERA neutrinos had much more energy than the ones from the supernova, but that would present even more problems.

Not being a particle physicist myself, I can’t meaningfully contribute to the discussions on theoretical implications of this experiment, if it’s actually true. I would, however, like to comment on how this story is unfolding from the point of view of the scientific method, and specifically how this story highlights the differences between real science and pseudoscience. I use “pseudoscience” to refer to homeopathy, energy healing products, reiki, dowsing, magnets, pendulums, astrology, and anything else that requires more “faith” than evidence.

In the wake of attending a New Age expo (out of morbid curiosity) and being overloaded with crackpots, quacks, and hucksters, these differences become all the more plain:

• The fact that the experimenters published any data at all is a sign of great scientific integrity. The fact that they held a press conference before the paper was peer-reviewed is a bit unfortunate, as noted by Lawrence Krauss, but I think the fact that this story made it to mainstream media outlets will help the general public understand the scientific process, as people follow the story. Pseudoscientists, on the other hand, seem to be allergic to data in general, and never publish anything.
• Essentially, the scientists of the OPERA experiment are saying, “We’ve gathered these data, we used the best possible experimental parameters, we’ve performed all the checks we could think of, and we still see this anomaly. So please, tell us what we did wrong.” This is surely science at its best! This is the kind of behavior that should be an inspiration for a whole generation of new scientists. We will never hear pseudoscientists utter that phrase.
• Real scientists don’t adhere dogmatically to any theory, no matter how foundational it may be. Even though most physicists agree that there was an error in the OPERA experiment, they still reserve a little room for the possibility that the results are correct, and that Relativity might be violated. Einstein to physicists is not the same as Chopra is to pseudoscientists.
• Real scientists expect extraordinary evidence for extraordinary claims. Most scientists agree that the evidence collected by the OPERA experiment is not extraordinary. Pseudoscientists make extraordinary claims every time they open their mouth, but present no evidence at all, except anecdotal testimonials from their friends and paid endorsers.
• If we read the blogs of popular physicists on the subject of the OPERA experiment, we find lively debates on theoretical explanations for the anomalous effect, and discussions on ways the experimenters miscalculated the speed of the neutrinos. The key point is: scientists get excited about the possibility of being proven wrong. Scientists can’t wait to be proven wrong, because it would mean that there’s more science to be done!
• Perhaps most importantly, real scientists are motivated by a desire to better understand our world. The only motivation of pseudoscientists is money, thinly veiled by a scientific-sounding sales pitch, and a nonsensical product du jour.

In any case, I encourage everyone to follow this story, because it’s a high-profile example of real science at work; a triumph of human achievement. No matter how the results turn out, by observing the process of scientific scrutiny, everyone will be better equipped to spot pseudoscience when it’s in plain sight.

I will update this post as soon as I see a quack energy-healing product that uses faster-than-light neutrinos to balance the flow of energy through your chakras. Post a comment if you find one yourself!

A case against accommodation

The biggest problem with religion seems to be that, no matter how moderately religious a society is, it inevitably creates a slippery slope towards extremism for those few adherents who take it a bit too literally; and there will always be those few. The reason for this is that religious moderates are basically the same as religious extremists, except that the moderates have (thankfully) allowed themselves to be tempered by the secular social norms of our time. By default, religious moderates are tolerant of extremists, because after all, the extremists actually believe what they say they believe, unlike the moderates who water down their religion to make it more palatable in the modern world.

And it seems to me that, from the atheist perspective, being an “accommodationist” would only help perpetuate that same kind of slippery slope that's already made abundant by the religious moderate majority.

My rhetorical question to the accommodationists would be, "To what end?" Surely there must be some extreme forms of religion that you're not willing to accommodate? If you're willing to accommodate some forms of moderate Christianity, or moderate Islam, but not the more extreme forms of the two, then that would be just as hypocritical as the moderate Christians who cherry-pick which verses of the Bible to take literally, and which ones to take metaphorically. Religion should be an all-or-nothing deal. When it's not all-or-nothing, there's always some hypocrisy to be found.

Speaking of hypocrisy, it feels like we have a certain amount of intellectual integrity at stake here. We atheists are, to a reasonable extent, certain about the truth of our convictions. I don't mean to speak for everybody, but that's generally the case; we arrive at certain conclusions with some amount of certainty, and we consider these conclusions "true," or at least tentatively true, insofar as the scientific method allows us to define truth. We don't "believe" in things in the same sense that religious people believe in things, because our conclusions are backed up by evidence and observations, which makes the truth of our beliefs that much more meaningful and convincing.

So, taking all of that into consideration, why on earth should we be accommodating toward beliefs that are clearly false, or beliefs that are clearly lies, or beliefs that are demonstrably harmful to the well-being of their adherents? What does it say about our intellectual integrity when we allow falsehoods to be perpetuated, no matter how much false hope or false happiness they might bring to the people who believe them? I would think that we should be doing our best to expose such beliefs for what they are, and uproot them from the consciousness of our society using tools like education, debate, and scrutiny.

There’s a theory of why religious people get so offended when their faith is questioned. And the theory is that religious people are actually embarrassed by the things they believe, but they just don’t consciously realize it, which is why they get so defensive when their beliefs are put under the microscope. It's embarrassing to believe the Earth is 6000 years old; it's embarrassing to believe that a woman can give birth to a child without a man's contribution to the zygote.

If I put myself in the mindset of a religious person, I can see how it would be embarrassing when science explains yet another thing that used to be attributed to God, and having my God demoted again and again, to the point where the very definition of "God" becomes so nebulous that it loses all meaning. And all I'm left with is profundities like “god is the universe,” or “god is beyond human logic,” or “god exists outside of space and time” -- that’s my favorite.

The thing is, for truly religious people, that kind of embarrassment is buried deep down in their unconscious mind. Instinctively they're perfectly aware that it's all nonsense. But those instincts have been repressed by their conscious religious training, or indoctrination, or whatever. So when those beliefs are questioned, the conscious mind has no answer, so it turns to the unconscious mind, which says that it's all nonsense, which directly butts heads with the conscious indoctrination, and that's where the defensiveness and the anger comes from.

That’s only a theory, anyway. But my whole point here is that our goal as responsible atheists should be to bring that unconscious embarrassment to the foreground of consciousness. Not just the consciousness of religious individuals, but the foreground of our social consciousness. It should become outwardly embarrassing to keep believing in an all-powerful creator god. It should become embarrassing to keep believing in prayer, or believing in hell or heaven.

Believing in a god is on the same theoretical footing as believing any other figment of imagination for which you would otherwise be called crazy. It just so happened that this particular god was the one that got ingrained into the fabric of our society. But aside from that, there's absolutely no reason that we shouldn't attach the same kind of negative stigma to people who believe in the Abrahamic god, or the literal truth of ancient folk tales.

I'm not saying that people shouldn’t be allowed to believe whatever they like; of course they should. What I am saying is, we should work towards creating a society where the moment someone considers taking religion literally, it should be readily apparent to that person how embarrassing, counterproductive, and unwise that would be. So, in that kind of society, no one would have a reason anymore to turn to religion for any purpose, so therefore no one would have a reason to go down the slippery slope toward extremism.

That's the kind of state we should be striving for; a state where it's just as embarrassing to believe in the god of Abraham as it is to believe in Zeus or Poseidon or Xenu; because they are all on the same footing of pre-scientific wishful thinking. And I don't see how accommodation will help us get there. Theism in general belongs in the Bronze Age, because it’s based on Bronze-age thinking, and because the Bronze Age is already the resting place for all other gods ever invented by men. There’s just one more to go!

When people who promote the merits of religion run out of arguments, they usually retreat to the last-resort argument, which is something like, “Well, at least religion gives people comfort, or hope, or a sense of purpose...” Well, that might be true; but the problem is that all those good things are for the wrong reasons, and all those things only happen when religion is at its very best. That's more like an idealization of religion; that's the infomercial promise of religion. The reality is quite different. In reality, when religion is not at its best, the same religion that brings the hope and the comfort will also bring fear, shame, intolerance, and guilt. And we know all too well what happens when religion is at its worst... it makes otherwise decent people commit unspeakably evil acts, for those very same reasons!

The other problem with that argument is that it’s rather condescending towards religious people. It assumes that religious people are too weak-minded to cope with the real world without religion, and I don’t think that’s true at all. I’m fully confident that even the most devoutly religious people will be able to find their moral bearings without a god telling them what’s right and wrong. I think people might be afraid to let go of religion, because religion has been pretty much the only option for thousands of years. But the solution to all of that, as with anything else, is education; not just education, but actively combating ignorance.

A proper education should start at the very beginning. Religion’s biggest offense is the indoctrination of young children. Nobody should have any kind of opinion or dogma forced onto them from birth, and yet this happens every day, in many millions of households, in the form of religious upbringing. I wish more of us would recoil when we hear parents label their young children as “Protestant” or “Jewish” or anything else, before the children are capable of objectively evaluating the implications of such a label.

That’s why I’m not advocating forcing atheism onto anyone. What I’m talking about is subtracting the forcing of religion (which is pretty much the definition of atheism anyway)! Atheism isn’t a viewpoint that can be forced onto someone. Atheism is a natural, “clean slate” state of mind, and children should be raised with a “clean slate” until they’re ready (and educated enough) to decide which ancient Babylonian deity to worship.

To put it plainly, we simply cannot afford to accommodate irrational beliefs anymore. It would be great to accommodate them, in theory, if only people’s irrational beliefs didn’t influence their actions, and if only people with irrational beliefs didn’t get elected to public offices, and didn’t allow their irrational beliefs to influence their policies. If that were the kind of world we lived in, then, by all means, accommodation would be very fitting and reasonable.

But we live in a country where half of the population refuses to accept basic facts about biology, and half of the population can’t tell you how long it takes for the Earth to make an orbit around the Sun. And we live in a world where we have an explosive growth of a religion that has a doctrine of military conquest literally built into it, and a growing minority of that religion that’s plotting our destruction as we speak.

We cannot afford to accommodate religions that are inherently anti-human, which all three of the world's "great monotheisms" absolutely are. The moment when a religion places more value on things that are supposed to happen after we die, rather than focusing on doing good deeds in this life for its own sake, is a warning sign that such a religion needs to be eradicated, and fast.

Our battle is nearly vertically uphill, and the last thing we should be doing is pretending that there’s any good to be found in letting people cling on to their irrational beliefs just a bit longer. Religion’s function has been to divide people, divide communities, and stifle scientific and intellectual achievement. We should be doing our best to phase it out, instead of accommodating it. To put it as charitably as I can, religion has been the training wheels of our morality. And at some point, training wheels become more of a hindrance than a benefit. Our civilization is long overdue to take the training wheels off, and throw them away.

However, the new film certainly had no shortage of plot holes and scientific inaccuracies. It's taken a while for me to crystallize my thoughts on it, but after watching it last week again on Blu-ray, I couldn't help but jot down a few nitpicks that really stuck out in my mind. Forgive my inner nerd for really showing in this post, and please feel free to contribute your own nitpicks in the comments, or criticize mine as you see fit! And, off we go.

A supernova that threatens the galaxy?

During his mind-meld with James Kirk, the elder Spock recounts the story that led to their current predicament.

According to Spock, a supernova explosion occurs in his time that threatens the survival of the galaxy. That's curious... what kind of supernova is this? Granted, supernova explosions are very luminous, but a single supernova would certainly not threaten an entire galaxy, and it certainly wouldn't carry the kind of planet-destroying force as shown in the film, at least not outside of a single star system.

Using our primitive Hubble Telescope, we have observed plenty of supernova remnants within our own galaxy that pose no threat to us whatsoever. The supernova remnants can grow to several light years in size, but that kind of distance is still minuscule on a galactic scale.

As it is depicted in the movie, Romulus is literally torn apart by the force of the supernova explosion. This means that it must have been the actual Romulan Sun that exploded. No stellar explosion can maintain that kind of force if it originated from a different star system.

It seems unlikely that Romulan scientists didn't anticipate their own sun going supernova many years in advance of the explosion. Stellar evolution, although not yet completely understood, is nevertheless fairly predictable. It should be relatively easy, especially for a warp-capable species, to tell if a planet's parent star is on the verge of exploding. Romulus could have been safely evacuated well before its star reached the end of its life.

Appalling Vulcan irresponsibility

I'm not sure I understand why the Vulcans felt it was their duty to contain the supernova. The Romulan star system is nowhere near Vulcan, so why was it up to the Vulcans to stop the explosion? OK, let's assume for a moment that Vulcans are the only species that has "red matter" technology, so they're the only ones who can stop the supernova by creating a black hole.

But wait... it's well-known that the Romulans use singularities (black holes) on a routine basis as a power source for their Warbirds, so the Romulans must be perfectly capable of creating black holes themselves! Couldn't they simply fling an abandoned Warbird into the supernova, and let the supernova be consumed by the black hole that powers the ship's warp core?

OK, let's assume that it was absolutely necessary for the Vulcans to handle this threat. In that case, it seems like the Vulcans handled it extremely irresponsibly, and completely contrary to logic.

Why was it the job of a geriatric diplomat (Spock) to deliver the red matter to the site of the supernova explosion? Was he going to negotiate a peace treaty with it? Couldn't they have sent someone more appropriate, such as a team of special-forces commandos, or at least someone in better health, or even an unmanned missile that simply plunges into the supernova along with the payload of red matter, much like Dr. Soran did with trilithium in Star Trek Generations?

Why is there so much red matter aboard Spock's ship? Seriously, if it only takes one droplet of red matter to create a black hole, why was there a comically gigantic ball of it aboard Spock's ship? That's enough to create a million black holes! Where else were they planning to use this much red matter?

The Vulcans should have anticipated that red matter could be used as a weapon of genocide. They should have recognized the staggering security risk of allowing red matter to come anywhere close to hostile territory. So why did they place their entire supply of red matter, capable of destroying a million planets, onto a virtually unarmed scout ship, and proceed to send the scout ship into Romulan space?! What did they think would happen?

All of this seems very irresponsible on the part of the Vulcans. Because of their short-sightedness, they've indirectly caused the destruction of their own homeworld, and altered the timeline for everybody else.

Black holes and time travel

In the movie, both Nero and Spock travel backwards in time by entering a black hole. Let me just slap my forehead a few more times. This is basically on the same theoretical footing as traveling back in time by performing a slingshot around a star, which made complete sense in Star Trek IV: The Voyage Home.

This isn't the first time that black holes were portrayed as portals through time in popular media. Black holes are certainly very interesting objects to theorize about, but they're not quite as exotic as they're made out to be.

Objects that fall past the event horizon of a black hole do not travel backwards in time. They simply fall closer and closer to the center of the black hole, until finally they're compressed to a single point of infinite density at the very center, adding to the mass that was already at the central point.

Of course, we don't yet have the physics to describe the nature of the infinite-density point at the center of the black hole, which is why it's called a singularity. But we do know that any mass that enters the black hole will remain in the black hole. It doesn't go backwards in time, nor does it go to another dimension, or another universe. All of the mass will remain in the central singularity for the remaining lifetime of the black hole.

Necessity of drilling

Why was it necessary for Nero to drill to the planet's core in order to drop the red matter? If the red matter really creates a black hole, it would suffice to drop the red matter anywhere on the planet's surface, and let the black hole consume the planet from the surface inward. Speaking of red matter...

Red matter?

Theoretically, any amount of matter can be turned into a black hole if it's compressed into a small enough volume (its Schwarzschild radius). For example, the Earth's Schwarzschild radius is about 9 millimeters. That is, for the Earth to become a black hole, it would need to be compressed into a volume with a radius of 9 millimeters (about the size of a grape).

Presumably, "red matter" is an exotic form of matter that automatically collapses beyond its own Schwarzschild radius when it's taken out of its containment field. Fair enough, but there are several major problems with this.

The most serious problem has to do with the size of the black hole that can be created with that amount of red matter. We can see from the movie that red matter is not particularly massive -- we see Spock and a Romulan handling containers with samples of red matter without exerting themselves at all. Since it took only a droplet of red matter to create a black hole, let's assume that the droplet's mass is 1 gram. The Schwarzschild radius for a mass of 1 gram would be about 1.5x10^-19 meters, which is several orders of magnitude smaller than the size of an atomic nucleus. A black hole of this size would pose no threat whatsoever, and this is for two reasons.

According to modern physics, black holes emit radiation with an intensity that is inversely proportional to their size. This is known as Hawking radiation, named after Stephen Hawking, who postulated its existence. If the black hole emits radiation, that must mean that it's losing energy, which means that it's losing mass, which means that it's getting smaller! And the smaller the black hole gets, the more intense (the higher temperature) its Hawking radiation becomes. This continues until the black hole completely evaporates in a blaze of glory consisting of ultra-energetic gamma rays.

The point is, if Nero used a tiny amount of red matter to create a black hole of the same mass, the black hole would evaporate with a flash of radiation almost instantaneously. The black hole would not go on to swell up and consume the planet.

Incidentally, the theory of Hawking radiation is one response to people's concerns regarding the possibility of creating a black hole at the Large Hadron Collider. Even if we create a tiny black hole at the LHC, it would instantly evaporate in a flash of radiation, and pose no further threat.

Also, even if black holes do not evaporate due to Hawking radiation, a black hole that's smaller than an atomic nucleus would have a hard time finding other matter to swallow up. It would take a long time indeed for such a black hole to have a noticeable effect on an entire planet.

Where's the Time Police?

This next nitpick doesn't really have to do with the movie itself, but with a different Star Trek story that inadvertently shot the entire franchise in the foot.

In the Star Trek: Voyager episode "Future's End," it's revealed that, in the 29th century, the Federation develops timeships that routinely patrol the timeline and attempt to eliminate any anomalies.

With this story, the writers basically negated any further possibility of having time-travel stories in Star Trek. If a starship travels back in time without "authorization," we should expect a visit from a temporal patrol ship from the 29th century. The patrol ship would then do whatever is necessary to correct the timeline, and all would be back in order.

In the Voyager episode, the timeship Aeon travels back in time to prevent the destruction of the Solar system. One would think that the destruction of Vulcan is an equally worthy cause for a timeship to investigate, and attempt to prevent. But, of course, we see no hint of this in the movie.

Sound in space

Having sound in space seems to be a sci-fi cliché that the writers and producers just can't unlearn, so it's not even a nitpick anymore. And, in all honesty, a little sound adds to the excitement of the space battle scenes, so it's not that big a deal.

However, in this movie, they actually made an attempt to get it right! I'm referring to the space-jump scene with Kirk, Sulu, and the unimportant guy who dies. When they jump off the shuttle and fall towards the planet, no sound can be heard. As they begin to enter Vulcan's atmosphere, more and more noise is heard around them. This is absolutely correct!

So why couldn't the movie take this excellent example and run with it, meaning get rid of all sound in the scenes where the shot takes place in outer space? All of the battle scenes and space explosions still have the usual sounds associated with them, without any regard for the fact that there's no medium for the sounds to travel through. But I digress.

Epilogue

Well, that's it for now, and thanks for indulging me. As I mentioned, this movie is a worthy successor to all the previous Star Trek films, as well as simply an excellent movie in its own right. I'm looking forward to the sequel(s).

In the meantime, all of the current sci-fi franchises, including Star Trek, would do well to hire some better scientific consultants. Maybe they can hire me?

Although White mentions that this is probably not the "true" 3D Mandelbrot, the new fractal is undoubtedly a sight to behold, especially considering the renderings he showcases on his webpage.

Unable to contain my enthusiasm, I quickly wrote up a small program that uses OpenGL to actually display this shape in 3D, in real time, to get a feel for what this beast looks like from all angles. Don't get too excited; the program does not render the shape in real time, it just displays the points rendered so far in real time. The actual rendering process can take a minute or so.

Download the program using the link below, and read further for instructions and screen shots.

Download the program! (or download the source code)

The program basically renders the 3D shape by constructing a "point cloud" that approximates the edge of the fractal.

Everything in the program should be relatively self-explanatory, but here's a brief overview of the features so far:

• The program lets you click-and drag the rendered shape to rotate it in trackball fashion (left mouse button), as well as zooming in and out (right mouse button).
• The program lets you select the "power" of the Mandelbulb formula, as well as the number of iterations to perform.
• The program lets you select the resolution of the point cloud.
• It gives you a "selection cube" with which you can select a subset of the shape to zoom in on (with the "zoom to cube" button).
• It has a number of other minor features like fog and anti-aliasing.
• It uses multiple threads to render the shape, so it will take advantage of multiple cores/processors.

Here are some additional screen shots:

The program was written in C# .NET, using the Open Toolkit Library (OpenTK) which provides an excellent OpenGL wrapper.

Of course, this program is very much in its early stages, so don't expect it to be perfect. As always, comments and suggestions are welcome!

The only problem I have with USB flash drives is when I mistakenly leave them in my pants pockets, and subsequently put the pants into the laundry basket. The flash drive will then suffer the grizzly fate of being spun around the washing machine soaked in soapy water, and will most likely never work again. This made me think about possible methods of somehow sealing the flash drive to make it more resistant to the elements, or to physical impact.

Background

At the office where I work, I had found a supply of epoxy that the hardware engineers use for various purposes. This epoxy comes in little packets, with each packet composed of two pouches containing different substances that, when mixed together, produce the hardening epoxy. I knew about the supply of epoxy for a while, but I hadn't made the connection between the epoxy and the flash drives until one day, in a moment of total enlightenment, I held up my flash drive in one hand, and an epoxy packet in the other, and began to laugh uncontrollably.

I wasn't sure yet how well the epoxy would work, but everything about the epoxy seemed perfect, including the quantity, and what was written on the packet, which is:

• Work time: 3 to 5 minutes.
• Will not shrink.

That same day, I took an ordinary USB flash drive, removed the plastic case so that the PC board was completely exposed, mixed up some epoxy, and poured it onto both sides of the board, making sure that all the electronic components were fully covered, and only the USB connector exposed. After about 5 minutes the epoxy hardened, and the result was even better than I hoped. The flash drive became indestructible!

Wanting to buy some of these packets for myself, I searched for a distributor of this stuff online. The brand of the epoxy is Hardman (aptly named!), and the first result is Ellsworth Adhesives, which sells a box of 100 packets for about $120. After looking a little harder, it seems that you can get the same box for a lot cheaper, such as from HMC Electronics which sells it for $80, which is 80 cents per packet -- a great deal. Plus, the box includes popsicle sticks for easy mixing and spreading.

After I received the box, I encased two more flash drives in epoxy, with the same great results. The epoxy becomes rock-solid and impenetrable! Since then, I've been epoxying pretty much everything that makes logical sense: more flash drives, card readers, MP3 players, etc. Take a look at this brief gallery of stuff that I've done this to:

[nggallery id=16]

Advantages

The benefits of epoxying a USB flash drive (or any other small USB device) include:

• It looks freakin' sweet
• It becomes virtually indestructible (the only remaining destructible component is the USB connector)
• It becomes waterproof. My current flash drive has survived five wash cycles! Of course you have to allow the USB connector to dry completely, but after that, it's as if nothing happened.
• The epoxy helps dissipate heat from the flash memory and controller chips.
• If the device has an LED, it will make the surrounding epoxy glow, which also looks cool.

Instructions

Here are some brief instructions for encasing your own USB flash drive in epoxy:

Safety first: Make sure you do this in a well-ventilated room, and don't get any epoxy on your skin or in your eyes. And of course, make sure any data that's currently on your flash drive is backed up, in case anything "unexpected" happens.

• Take apart your USB flash drive. This is usually as simple as pulling apart the plastic cover that encases the PCB (printed circuit board). Be careful not to damage any of the delicate electronic components that are soldered onto the board. Throw the plastic away. All you should have left is the PCB with a USB connector soldered to it. If you like, you can write your initials on the PCB with a felt-tip pen, so that they'll be visible through the clear epoxy when you're finished.
• Mix up some epoxy. I would recommend using two packets of the Hardman epoxy for an average-size USB drive (one for each side of the PCB). I usually mix the epoxy with a popsicle stick, on top of a sheet of aluminum foil. The epoxy must be mixed very thoroughly, or it won't harden uniformly. However, don't take too long to mix it, since it will begin to harden very quickly.
• Hold the flash drive by the USB connector, allowing one side of the PCB to face up (you'll repeat this for the other side), and spread some epoxy right onto the exposed PCB with a popsicle stick (or your tool of choice)! Keep adding epoxy until all the electronic components are completely covered by it, right up to the connector (don't put any epoxy on or inside the connector itself). Do your best to keep the epoxy well-contained. It can get messy fast.
• Keep holding the flash drive with the epoxied side facing up, so that the epoxy settles evenly throughout the surface of the PCB. If some of the epoxy starts to drip off the edge, let it drip, or scrape off the excess with the popsicle stick. The epoxy creates an exothermic reaction while setting, so it might get a little warm, but don't be alarmed -- it won't get too hot to touch. Don't let anything come into contact with the epoxy while it's setting, so that you'll get a smooth, glossy surface.
• After holding for a few minutes, the epoxy should harden, at which point you can flip over your flash drive and repeat the procedure on the other side of the PCB.
• When the epoxy on both sides of the PCB has hardened, you're done! You might want to wait an additional 24 hours for the epoxy to really harden, though.
• Enjoy your flash drive, which is now stronger than ever, looks slick, and is completely impervious to the elements!

So, then, aside from USB flash drives, what kind of things are you planning to (or have already) encase in epoxy?

(Thanks to Lifehacker for picking up this story)

This book is especially significant in one other way: it contains my artwork! The book's entry on Knight's Tours (p. 186) familiarizes the reader with the history of this problem, dating all the way back to Euler in 1759. And, alongside the article, Pickover displays a 30x30 knight's tour that was solved by my neural network knight's tour implementation. For the picture in the book, I used a modified version of the program that generated a sufficiently hi-res image. That particular knight's tour took about 3 days for my computer to generate.

I'm deeply grateful to have one of my creations published in a book by someone as influential as Cliff Pickover. Of course, it's all of the 250 entries in the book that make it an incredibly fascinating stroll through the history of mathematics. As mentioned elsewhere, this book definitely has bestseller potential, and could easily be one of Pickover's best works. Buy the book now!