Moroha　諸刃

Cyber-bullying and such has recently come into the consciousness and lexicon of the internet-using west. Incidents like the Star Wars kid or more tragically Megan Meier have made us more aware and wary of what us and our children are doing online.

In East Asia though, there is another type of cyber-bullying that hasn’t really been noticed so much here in the west yet. It’s called internet vigilantism, and this is where seemingly the entire internet attacks someone online, leading to real-life consequences.

There are cases of internet vigilantism in the west, but there has been almost no backlash against it because it’s almost always directed towards individuals that have committed fraud, theft, or pedophile crimes. 419 Eater is famous for baiting Nigerian scammers, and Anonymous/4chan (No link for 4chan. You don’t want to go there. Really, you don’t.) has baited and outed pedophiles in the past. Similarly there have been internet blitzes against people that have thrown dogs off of a cliff. Generally this kind of internet vigilantism results in people working to 1) identify the perpetrator 2) make their identity public, and 3) alert law enforcement. Especially in the case of the dog-throwing soldier there were also numerous death threats, etc., but overall the internet vigilantism served to bring the criminals to justice.

This isn’t how it’s been working in Asia, especially Korea. This article calls it ‘witch hunting’, which is perhaps a better term because many of these cases were not against criminals, but against normal people that had done something that people found offensive. The above article mentions the ‘loser girl‘:

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One of the more interesting skills learned as an engineer or a scientist is the art/skill (it’s really both) of being able to make reasonable order-of-magnitude estimates. Using a combination of knowledge, common sense, reasoning, intuition, and some quick hand calculations, a skilled engineer/scientist will often try and estimate the critical parameter or result of some system before going through the tedious calculations to get a more accurate answer. This is useful for several reasons: it gives you an idea of what orders of magnitude you will be dealing with, it gives you a ‘sanity check‘ for when you calculate a more accurate answer, and most importantly, often times an order of magnitude estimate is all that you really need.

This process is sometimes called handwaving, back-of-the-envelope calculation, guesstimate, or a ballpark estimate. They are also sometimes called Fermi problems, since the physicist Enrico Fermi was renowned for being able to perform such simple estimates and get within a factor of 2 or 3 of the actual answer (this is extremely good for a simple estimate). Two famous examples of are his calculation for how many piano tuners there are in Chicago, and his estimation of the energy yield of the first atomic bomb test by dropping some scraps of paper and seeing how far the blast blew them.

Often times when you are making such estimates, you simply round (logarithmically) each number to it’s nearest power of 10. This is because your estimates are off by factors at least that large anyway, so there’s little point in carrying through precise numerical calculations. A personal favorite anecdote on this principal came from my brother Porter when explaining why he replaced with the number 1, “Why did I make equal to 1? Because it’s not 10.” (In actuality though, since and , is right close to the dividing line between assigning it to the value of 1 or 10. You can choose either, or just make it 3, which is what I usually do.)

The reason why I’m talking about this is because today I stumbled upon this page for a class at MIT that deals entirely with this subject. The name of the course? “Lies and Damn Lies: The Art of Approximation in Science”. I skimmed through the first chapter and it was very well-written and interesting. You could learn a lot about this skill just by reading the chapter and working through the problems yourself.

Another closely related but slightly more accurate method of estimation uses dimensional analysis. The wikipedia article I linked to is a bit obtuse for the uninitiated, but the two examples halfway through the article are fairly simple to follow and stand well on their own. For dimensional analysis you use your knowledge of the underlying physics of a system to make reasonable assumptions about what parameters are pertinent in your analysis. A more mathematically formalized version of this is called the Buckingham π theorem, and is an extremely useful and versatile tool for the initial analysis of a system.

My favorite example is at the end of the article, where it shows how Geoffrey I. Taylor used the Buckingham π theorem to estimate, again, the energy output of the first atomic explosion. A summation of his original paper with his analysis can be found online. Basically he was able to determine the following relationship:

,
where R is the radius of the exploding shockwave at some time after detonation, t is the time, p is the atmospheric pressure and E is the energy released upon detonation. He used recently declassified movies of the explosion to get the radius and time values, and that allowed him to estimate the energy. In fact, when he published his results it caused quite a commotion in the US Defense Department because the energy output of the atomic bomb was still classified at the time and Taylor’s result was far too accurate for their liking!

In my never ending quest to understand a little more of the Japanese language (and never succeeding because I never invest enough time in it), one thing that consistently frustrates me is old and ancient script. In the title wrote Chinese/Japanese because 1.) The Japanese kanji come from Chinese as everyone knows, and 2.) For many centuries after writing was first introduced to Japan from China, all writing in Japan was done in Chinese. In Japanese this is called kobun (古文, lit. old writing), and as Westerners we may think of it as analogous to medieval and renaissance Europe where all scholarly work was done in Latin, regardless of whatever language you might actually be speaking (i.e. Newton’s Principia Mathematica was written in Latin).

I have no hope of reading this ancient Japanese/Chinese, but that’s actually not what I’m referring to. I’m instead talking about the old way to write the characters. Just like how vocabulary and grammar for a language evolve and change over time, so did the way of writing the characters. In this picture from Wikipedia you can see the evolution of the character for tiger.

So even if I’m not trying to read ancient Japanese or Chinese texts, the old style of writing still shows up fairly frequently (similar to how old Gothic and Latin scripts and such still get used in English), but they can be nearly impossible to read, even if you can read the modern form of the character! One place they show up fairly often is in seals. In Japanese legal documents, instead of signing with a signature, you place a red stamp with your official seal (think of royalty using their signet ring to seal letters and documents). In order to prevent forgery, ideally your seal is hand made by a licensed seal craftsman so that it is unique, and then the seal itself is registered in your name at the government offices. The characters often used on these seals are called seal script, and it is the style that evolved during the Qin dynasty of ancient China. Some examples of seals using the seal script I got on google search are here, here, here, and some here.

For example, here are two seal script characters:

If I hadn’t looked up these specific two characters, I would have no chance in reading them even though their modern forms are characters I am very familiar with. In fact, the modern form of these two characters is:

Which is in fact the name of my blog, moroha.

So the question is, where did I look these up? Japanese dictionaries invariably never have them, but I did find a Chinese/English language site that has them. Just put the kanji you want to look up in the blank and click the button that says Etymology, and it will give you the modern character in both traditional and simplified Chinese, in addition to all known variants of seal script, bronze script, and oracle bone script (the really old stuff). As long as you’re using unicode the characters are interchangeable, so you can still do the input in Japanese.

For some real craziness, check out all the old variations for the character of horse, one of the oldest. All this craziness about having many different ways to write the same character was one thing that the 1st emperor of China, Qin Shi Huangdi, tried to do away with when he standardized the writing system for all of China.

Any geek that grew up in the 80’s or 90’s probably remembers the X-men cartoon that was on during the 90’s. The animation wasn’t all that great, but it was still entertaining for this teenager at the time. The intro here may bring back a few memories:

I just saw something that blew my mind though. In a rare exception to the norm, the X-men cartoon was ported and re-dubbed for a Japanese release. Here is the Japanese intro:

First of all, that heavy guitar J-pop totally reminds me of the theme to Fist of the North Star, which I have blogged about before, even starting with “Shock!” which is all too similar to Fist of the North Star’s “You are shock!”. There are also some weird inconsistencies like Magneto summoning the Brood, Cable in power armor, etc., but I’m not familiar enough with the Marvel universe to comment on them.

I can however, comment on the lyrics for the theme song. According to Wikipedia, the song is ライジング (Rising), by the Japanese band アンビエンス (Ambiance). Here are the lyrics and my attempted translation in parenthesis:

Shock!　嘘で固めたナイフ切り付け (Shock! Cut with the knife hardened by lies)
Shock!　夢を飲み込み街は輝く (Shock! Catch the dream as the city shines)
争いや憎しみで　その身削られてゆく (The conflict and hatred cut away at you)
真夜中襲いくる　人知れぬまま (They attack unseen in the night)
Break Out!
ライムライト　光るざわめき (Commotion in the limelight)
リアルタイム　濡れた幻 (Real-time wet illusion)
Cry for the moon

The translation is quite hard (for me, at least) because as often happens in song lyrics and poetry in general is that many particles (similar to prepositions, they identify the part of speech the word or phrase is) are completely omitted, so I have to guess what the relationship is between the different words. Those last two lines are the hardest, as they don’t make any sense to me, especially the 濡れた幻 (wet illusion). What in the world is that supposed to mean?

Although, that “Cry for the moon” at the end is pretty awesome.

Sometimes you see something on the interblags that is so awesome you have to share it, even though everyone has probably already seen it before you. This is one of those things. Yesterday I discovered the music videos of L. B. Rayne. He’s like some kind of parody/homage to 80’s adventure movies and electronic music. So far he only has two videos that I can find though. The first is Indiana Jones: The Lost Theme Song:

I first heard about L. B. Rayne over at TR though, where they showed his newest video, Skywalking.

A couple of years ago I wrote a post where I talked about taking the imaginary number i to it’s own power an infinite amount of times, essentially

.

I showed numerically at least that it converges upon a single value in the complex plane, but then I speculated about what would happen if I did the same for other numbers? I thought it would most likely be a fractal like the Mandelbrot set or the Julia set, but I never got around to actually solving it.

Well, for the class that I’m TA’ing this semester (intro to computing for Chemical Engineers), I got hold of some simple code for making the Mandelbrot set in MATLAB to show the students a fun and interesting example of using for loops. After I did that though, I figured that it would be fairly simple to modify the code to see if taking a complex number to it’s own power created a fractal or not. So my algorithm was the following:

For any point c in the complex plane, let

.
In the limit as n goes to infinity, if z remains finite, then c is within the set. Otherwise it is not in the set.

Since you can’t really evaluate it to infinity, what you do instead is implement an algorithm where you perform the iteration a large but finite number if times, and see if the iteration stays inside a set radius. So here is my fractal. The first plot shows the the complex plane from -20 to +20 on both the real and imaginary axis:

Here the blue football-shaped region in the center is centered at the origin. These points are considered to be ‘within’ the set, since a large number of iterations did not give numbers that were outside of the convergence radius (I set the number of iterations to 50, and the convergence radius to 1000). Any points that are not that deep blue are considered to be ‘outside’ the set, with the color being an indication of how many iterations it took for that point to leave the convergence radius. The dark red points took the least iterations, with the orange, yellow, green, and light blue areas taking progressively more iterations.

I think the feathery wing structures going in the positive and negative imaginary directions are really interesting. They continue up and down seemingly without end, or at least I didn’t see any end for even large plots that I made. This is in sharp contrast to the Mandelbrot and Julia sets which are confined to a finite area.

But the center looks the most interesting, so let’s get a closeup of that.

There’s a lot of interesting stuff going on in this area, with some really beautiful feathery wings, and a jumbled area that just looks like ’static’. Here’s a zoom-in that let’s us see a little bit of both better.

Wow. Those feathers really are quite beautiful if I do say so myself. That random static-looking area bugs me though, since random noise really isn’t a feature of fractals. Instead they exhibit more of an ‘ordered chaos’ showing infinite complexity. So for my last image here is a much closer zoom on the static-looking area.

This last image has a width and height of just 0.005. Here we can see that it really is infinitely complex and not just random noise. I did another with a width and height of 0.0005, and it looks very similar, so there is some degree of self-similarity, much like we see in other fractals.

So the only thing this set is missing is a name. In reality probably someone has calculated this set and given it a name, but on the slight chance that no one has, I hereby name it the Bassett set. (How’s that for hubris? I bet Benoit Mandelbrot didn’t name the set after himself, but that someone else named it after him in honor of his discovery)

I was chatting with my brother Porter the other day and he told me how he made a Tower of Hanoi game for his children to play with. It’s a fairly simple game with a well-known binary sequence to solving it, in fact it’s one of the few puzzle games where the God’s Algorithm (a shortest-number-of-moves algorithm that can be mathematically proven) exists and is known. The shortest-path solution takes exactly moves to move the disks from one post to another. Porter mentioned in his next blog post that him and his son then calculated how high of a stack The Flash could do if he could move 1 million disks per second, and concluded that it would still take him longer than the age of the universe to complete the 100-disk version.

That’s a good start, but any self-respecting geek has to take things a notch further. First I needed to derive a formula that let’s me calculate how high of a stack I can complete in a given time given a rate of how many disks per second I can move. The original equation we can rearrange as:

,
where N is the number of disks, and n is the number of moves. Then we can replace the n with , where is the frequency of number of moves per unit of time, and t is the total time. So now our equation is:
.
You may notice that I have ignored the . This is because the will be so large that we can ignore the the , as it is inconsequential.

This formula let’s us do some basic calculations. If we take t to be the age of the universe in seconds (about ) then we have the following number of disks we can expect to complete within that time for the given number of disks moved per second:

So we can see that if an immortal Flash were to move disks for the entire age of the current universe at the rate of 1000 disks/s, then he could only expect to complete a stack of 68 disks. Increasing it to 1 billion disks/s only increases it to 88 disks! Still a far cry from completing 100 disks.

So the next question is what kind of energy/power requirement would we need to move the disks at these kind of rates? First we’ll need to make some assumptions on mass and distance. One typical move is shown in the animated gif below (if someone knows how to set it so that it will repeat more than once, please let me know):

In terms of mechanics, to move the disk from column one to column two the disk has to do six steps: 1) accelerate up until its halfway up the column, 2) decelerate until it comes to a stop having just cleared the column, 3) accelerate horizontally until its halfway to the next column, 4) decelerate until it comes to a stop above the new column, 5) accelerate down until it’s halfway down the new column, and finally 6) decelerate until it comes to a stop in the new position.

Now you may say that we don’t need to decelerate the disk as it reaches its resting point and just let it smack into the resultant stack, but when the speeds become really fast the energy will be enough to obliterate any disk, so we’ll include the final deceleration. We’ll also assume this is done in a vacuum so we can ignore wind resistance, otherwise the heat would be more than enough to ionize the disks (those that have read the well known Physics of Santa will be familiar with this). At some point the acceleration alone will become greater than the structural integrity of the disks, as well as relativistic effects at some point coming into play. We’ll get to those in a moment. For now though, we’ll simplify the 6 steps above by making them all the same length for every step. We can do this by putting the three columns in a triangular arrangement and then saying the disks are thin enough that we can neglect the change in the height of the stack as we make progress. We’ll say the columns are 10 cm apart and 10 cm high, so each of the 6 steps will be 5 cm. Also we’ll say each disk weighs 100 g.

Using classical mechanics (ignoring relativistic effects), the time to complete one step is simply 1/6 of a move, so that is:

.
The maximum velocity attained (so that we can know if we’re getting close to relativistic speeds) is:
.
The acceleration the disk undergoes (to see of we are overcoming structural integrity) is:
.
The energy required to complete one step is:
.
And finally the power required to keep the disks moving is:
.
Putting all these together in a handy chart we can see the results.



And the results are pretty interesting. We can determine what the trends are with the formulas above, and we can see how the various values scale with the frequency by replacing t in the equations with . That gives us the following scaling arguments: , , , and . In other words, if we double the frequency of the steps we will double the maximum velocity, but the acceleration and the energy will change by 4x, and the required power will change by 8x! This comes out to be a huge power requirement for the higher frequencies.

To get an idea of how huge the power requirements become, here are some power equivalents on the same order of magnitude:
To get , you would need the power consumption of about 10 DVD drive lasers.
To get , you would need the electrical output of a 1×1 m solar panel in full sunlight.
To get , you would need the power output of a typical automobile.
To get , you would need the power output of a Boeing 777.
To get , you would need the total power received by the earth from the sun.
And to get , you would need about 1/3 the total power output from the sun.
(All order of magnitude power estimates are from this Wikipedia page.)

How does this highest frequency look with our other limits on velocity and acceleration? We should be OK on velocity, since is still only 1/5 the speed of light, slow enough that we can still ignore relativistic effects. As for the stress that the object undergoes due to acceleration, that’s fairly simple to calculate too. Stress is simply force over area, given in this simple formula:

.
Where F is the force and a is the cross-sectional area. We can get the force from Newton’s 2nd law: . For the area we will need to assume a cross-sectional area of the disks themselves. Assuming the disks are about 3 cm in diameter, that gives about 7 in area. Calculating the stress that each disk receives we get the following:

Looking up the strength of various materials, the highest two were for high-impact steel and diamond, both being around 1 GPa . So from the table, we could expect to move 1000 disks per second, but the disks would fail due to the acceleration if we tried to go much faster than that.

Assuming that we could make disks out of impossibilium that can take any amount of stress, then for The Flash to complete a Tower of Hanoi with 88 disks, he would need to move 1 billion disks per second at a speed of about 1/5 the speed of light for 10 trillion years, and he would require the constant power output of about 1/3 of the sun (or a series of equivalent-sized stars, since a single star won’t last that long).

That’s it for this post, in the next post I’ll try to include relativistic effects for even faster speeds.

Overall, I consider myself to be fairly tech-savvy. I program in multiple languages for my research (right now: python and MATLAB, though I have used C++), I use both windows and linux systems (though I’m still not entirely comfortable in linux I’m getting there), and when I have computer problems both software and hardware I can usually diagnose and fix the problem.

However, when it comes to new trends on the internet, sometimes I can be quite a Luddite. I still have yet to register on facebook/myspace (I can’t remember which one is considered ‘cool’ and which is considered ’stalker’s playground’), and I have no desire whatsoever to ‘tweet’. I blog is only intermittently updated, and its traffic is somewhere near the bottom of the internet. I’m fine with that, since notoriety on the internet is definitely a two-edged sword.

A couple of days ago though, I finally decided to start using RSS feeds for checking websites. My morning internet routine has grown to include several dozen websites, and many of them only update every few days. There are other sites that update less than once a week, and I always forget to check them by the time the next week comes around. (The ones that update many times a day, like Fark, Reddit, and Digg I had to quit cold turkey. They were just sucking up too much time).

So I broke down and registered on google for their google reader service, and started registering for RSS feeds. It’s amazingly simple and it works very well. I just wish I had tried it earlier. Another thing that I found it is great for is keeping track of the latest research. Not only do many research journals have RSS feeds, but some of the larger databases for scholarly research will let you do an RSS feed on search results, so that if a paper that matches your search criteria is published in any of the journals in their database, they will send a link to you. I think it’s a great idea and I hope I can get a lot out of it.

One of the things that I enjoy about going back to Japan for a few weeks each summer is that it allows me go to to the bookstore and purchase some new reading material in Japanese. Now my Japanese is decent but not great (I would guess if I took the Japanese Language Proficiency Test that I could pass the level 3 easily without studying, but I would need to do a bit of studying to pass the level 2), so I can’t just pick up any book and start reading it. For me reading “real” Japanese is still a fairly laborious affair with a dictionary, and it goes pretty slow.

That’s why I like the light novels. They are very similar to young adult fiction here in the U.S. in that they are (more so in the U.S.) generally marketed towards a younger audience, the books are shorter, and the language is simpler than what you would find in a real ‘literature’ novel or a newspaper article or such. Another nice feature is that many of the more difficult words it does contain also have furigana, which gives the phonetic pronunciation of words using kanji, making it easier to read, or at least much quicker to look it up in a dictionary.

What got me started reading them was when Ryoko started buying and reading the novels for Full Metal Panic!, because she loved the anime so much. I started reading them myself and found that although I read them much slower (It can take me several days or weeks to finish what she can do in 4~5 hours) I was able to pretty much fully comprehend everything with frequent help from a dictionary.

So when we went back to Japan, I decided I would try some other series. The problem is though, there is almost too much to choose from. The light novel section in any bookstore is quite large, and is generally surpassed only by the manga section. (Helpful tip: while most bookstores have taken to shrink-wrapping the manga to keep loiterers from spending hours just reading manga in the bookstore, they don’t do that with the light novels. Yet.) Without knowing what to look for, I just kind of chose some at random. (Although I was able to avoid the ones that are more risque, they’re easy to spot by their cover art.)

The three I picked (this was last year) were all the first book from 3 different series. The first was a vampire story called Black Blood Brothers, the second was a high fantasy series called ダークエルフの口付け (Kiss of the Dark Elf), and the third was called とある魔術の禁書目録（インデックス） (A Certain Magical Index).

Those of you in the know on anime will recognize the first and the third since they have subsequently been produced as anime series, but probably not the second since it doesn’t exist in any other form.

This may actually be unfortunate for Black Blood Brothers, because the consensus I’ve heard about the anime (I haven’t seen the anime myself, only the novels) is that it was done cheaply by a low-quality studio and hence pretty much sucked. I think that’s too bad because from what I’ve read so far (the 1st 2 volumes, and there are many more to go) it has a lot of potential. The author sets up a really interesting premise (read the blurb in the wikipedia page linked above) and goes with it. I think this author’s strong point it the action scenes: they were really exciting and fun to read, and I kept on cursing my slow eyeballs, wishing I could read the Japanese faster.

As for Index, the premise is a little strange. The protagonist is your typical “Ordinary High School Student“, but lives in a world where psychic powers and actual magic seem to exist simultaneously. I’ve heard the anime based off of this series was done pretty well, so I’m looking forward to watching it after I’ve read it.

The Dark Elf series has two protagonists: The title character is a dark elf named Bela (they always use the word ‘dark elf’, it seems that the word ‘drow’ has never made it over into Japanese fantasy vocabulary), and Amadeo, your typical young, eager, and inexperienced human male adventurer. I should mention that this story takes pace in the Sword World official campaign world, similar to how here in the US we have fantasy books that take place in the Forgotten Realms or Dragon Lance world. The author spins a very complicated web of intrigue and conspiracy that involves the two characters. In fact it gets so complex that by the second novel in the series, the author provides a diagram so that you can keep track of the characters and their relations with each other. (Oh how I wish the Wheel of Time had such a study aid. A google search for ["wheel of time" "too many characters"] gives 387,000 hits.)

So these books aren’t exactly Nobel Prize quality literature, but they are good for my level of Japanese. I can read them just fast enough that I’m able to stay interested in the story.

As a speaker of Japanese and English, I find this hilarious. Translation Party is a site that uses the Google automatic translation to hilarious effect. Now the basis is nothing new. Ever since Babelfish came out, people have been using it to translate phrases from one language to another and then back again to hilarious effect. Where this one differs though, is that it repeats the double-translation until the English phrase it gets back is the same as the one it used in the previous iteration. In other words, it translates until it reaches convergence.

For simple phrases it does pretty well. But for more complicated ones it can come up with some really bizarre results. Here’s a tough one I gave it, a couple of lines from the Camelot song in Monty Python and the Holy Grail:

“In war we’re tough and able, quite indefatigable, between our quests we sequin vests, and impersonate Clark Gable.”

The result? “Patience in the war, KURAKUGEBURU spangles to impersonate a good idea to explore is difficult.”

The all-caps KURAKUGEBURU is just Clark Gable. For the first Eng->Jap step it does a pretty good job translating the proper noun into its katakana equivalent, but evidently the English dictionary does not have Clark Gable in it, so it just leaves it in all caps and anglicizes the Japanese pronunciation.