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We live in an interesting time where new technologies are radically reforming how humans interact with machines and with each other. The field of education is no exception. Tech savvy teachers are likely to be familiar with new educational paradigms like BYOD, MOOC, and flipped classrooms. There’s more to this movement than just fancy buzzwords. Teachers are forging ahead into new territory by bringing technology into the classroom and looking for ways to make the most of it. As these technologies continue to improve, these hi-tech classrooms are starting to look like something out of a science fiction story.

Many scientific advances have had their roots in science fiction. It seems pertinent then to examine how science fiction authors have depicted the future of education as a source of inspiration for the hi-tech classroom. In this post, we’ll take a look at some Sci-Fi classrooms and see what lessons we can learn from them.

The sources

The following are a collection of Sci-Fi classrooms from sources that I’m familiar with. I’m sure this list is not exhaustive, so please feel free to contribute others in the comments. Also, please note that some of these source materials are intended for mature audiences. I’ll try avoid any major spoilers for those who are unfamiliar with them.

Starship Troopers

Based on a novel by Robert Heinlein, Starship Troopers takes place in a future where democracy has crumbled and replaced with a militarist establishment. Humanity is engaged in an interstellar war against alien species, and enlisting in the military is the most efficient path to “citizenship”.

The beginning of the film depicts the protagonist, Rico, in a high school history class. Despite the futuristic setting, the classroom largely fits the “traditional lecture” paradigm. Rico’s history teacher is a retired officer who is missing an arm. The course is arguably equal parts history and propaganda.startshiptroopers3

While there isn’t much use of technology in the classroom, each desk seems to have a touch sensitive computer embedding in it.  For Rico, this seems to be more of a distraction from the class than a learning aid.

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The high school experience ends with high stakes testing.  A low math score ultimately places Rico into the infantry while his close friends are placed in flight school and military intelligence.  For added pressure, students seem to check their test scores on a public computer terminal.

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We also get a glimpse of a futuristic biology lab, in which students dissect alien lifeforms.

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While the lectures, labs, and high stakes testing are all too familiar, the film does raise interesting questions about the purpose of education. The school is structured like a factory to produce potential soldiers. It’s easy to see why this militaristic society would structure education in such a way that cultivates students that efficiently follow orders. I tend to view this as a cautionary tale of what education might become in the hands of a powerful military bureaucracy.

WALL-E

WALL-E follows the adventures of a trash compacting robot in a world where Earth’s natural resources have been extinguished by rampant consumerism. With the Earth no longer capable of supporting life, the remaining population leaves the planet in large intergalactic cruise ships. In the film, we observe a brief scene depicting a futuristic pre-school.

In this scene, a number of small children are watching a video with a computerized narrator describing the letters of the alphabet. No adults are present in the room and the instruction is fully provided by a robot. This picture of education fits with the overall premise of the film, in that humans have essentially automated themselves into irrelevance.

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Like Starship Troopers, the educational system is designed to perpetuate the existing authority. Even in this pre-school setting, students are conditioned by messages such as “B is for Buy-N-Large, your very best friend”. It’s implied later in the film that the residents of this spaceship are taught very little about life on the planet that their ancestors fled. The system is programmed to keep the residents living happily on the ship, and inhibiting any curiosity about to the circumstances that put them there. The residents are fat, happy and ignorant, and the fully automated educational system is designed to keep them that way.

Serenity

Based on the Firefly TV series, Serenity treats us to a brief glimpse of River Tam’s childhood. The young River has been identified as intellectually gifted and is sent to “The Academy”.

In this scene, River is taking part in a history course. It begins with the teacher narrating in front of a holographic projection that displays a visual depiction of the events. The lesson describes the “Unification War”, in which a number of planets rebelled against the Alliance’s expansion. The teacher explains that the Alliance engaged in this war to spread peace throughout the galaxy and asks why the rebels would resist. River seems to suspect that there’s more to the story and points out that “people don’t like to be meddled with”.

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While this looks like a typical lecture classroom, each of the students appears to have touch sensitive computer screen embedded in the desks. Students seem to be interacting with the computer during the lecture using a stylus, but also are engaged in note taking with a traditional pen and paper.

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We later find out that the Academy is actually a front for a program to turn these students in super-soldiers through a series of cruel medical and psychological experiments. River’s skepticism of the Alliance’s meddling turns out to be quite prescient.

Star Trek

In the 2009 film Star Trek, we find one of the more visually striking Sci-Fi classrooms. A young Spock is depicted in a school for Vulcans, a race known for their strong devotion to logical reasoning.  The scene shows students in semi-spherical pods, where the students interact with a projected display.  Several adults can be seen walking between these learning pods, but the main source of instruction appears to be with the computer.

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The computer asks the students various questions, particularly involving science and mathematics, and the student responds verbally with the answers.

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As the young Spock completes his interactive instruction, he is met by several other students who proceed to bully him about his human mother.

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The young Spock fights back out of anger, a course of action which is looked down upon in a society that values emotional restraint.

 

Star Trek: Voyager

Within the Star Trek universe, the TV series Star Trek: Voyager provides another perspective on education. The star-ship Voyager gets lost in space after travelling through a worm hole and spends many years heading back home. In this time, one of the crew-members gives birth on board the ship. The child, Naomi Wildman, grows up aboard the star-ship and is essentially home-schooled by the crew.

The details on Naomi’s education are limited, but she takes a liking to the Borg crew-member Seven of Nine who serves as a mentor. On occasion, Seven will assign her various instructional materials or ask her to carry out small tasks on the ship.  Several other crewmembers serve as teachers as well.  Naomi works diligently on these tasks and aspires to become the Captain’s Assistant.

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We also know that Naoimi spends a good deal of time on board the ship’s holodeck. It’s implied that some of Naomi’s education comes from interactive holographic children’s tales like “The Adventures of Flotter”. This colorful interactive fairy tale is designed to teach children deductive reasoning skills, and Naomi needs to solve several puzzle to help the storyline progress.

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In a later episode, the crew picks up several Borg children and the educational offering on Voyager are expanded to meet their needs. This results in the First Annual Voyager Science Fair. Naomi presents a model of planet, while the Borg children present a clone potato, an ant colony and a gravimetric sensor.

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Accel World

Accel World is a manga and anime by Reki Kawahara set in a future where humans can interface with computers via a “Neuro-Linker”. This hardware allows individuals to interact in a virtual environment using thoughts to control their personal computer. The opening episode of Accel World depicts what looks like a typical classroom: a teacher at the front of the class lectures while the students are busy taking notes. The difference is that the teacher isn’t actually writing on the board, but rather the hand movements of the teacher are transcribed to a digital blackboard which the students can see through the neural-interfaced computer.

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We also see that all of the students are busy using hand gestures to control these computers throughout the class.

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Like Star Trek, the synchronous nature of the classroom causes problems for the protagonist. Haru is short fat kid with low self-esteem who is regularly bullied by students that are bigger than him.

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To Haru, the virtual reality system provided by the Neuro-Linker is his only escape from the hostile environment of reality. When a classmate offers him a strange program that will “destroy his reality”, he eagerly seizes the opportunity.

Ready Player One

Ernest Cline’s novel Ready Player One takes place largely within an interactive simulation called OASIS. In a world that has been ravaged by climate change and a crumbling democracy, the brick and mortar schools are a potentially hostile environment and the protagonist, Wade, volunteered to pilot an educational program in this virtual environment. Users access the OASIS using a combination of a virtual reality visor, haptic gloves (and other accessories) and voice control. Wade’s school is one of many in OASIS and he describes some of the advantages of a virtual school:

There were hundreds of school campuses here on Ludus, spread out evenly across the planet’s surface. The schools were all identical, because the same construction code was copied and pasted into a different location whenever a new school was needed. And since the buildings were just pieces of software, their design wasn’t limited by monetary constraints, or even by the laws of physics. So every school was a grand palace of learning, with polished marble hallways, cathedral-like classrooms, zero-g gymnasiums, and virtual libraries containing every (school board–approved) book ever written.

On my first day at OPS #1873, I thought I’d died and gone to heaven. Now, instead of running a gauntlet of bullies and drug addicts on my walk to school each morning, I went straight to my hideout and stayed there all day. Best of all, in the OASIS, no one could tell that I was fat, that I had acne, or that I wore the same shabby clothes every week. Bullies couldn’t pelt me with spitballs, give me atomic wedgies, or pummel me by the bike rack after school. No one could even touch me. In here, I was safe.

When I arrived in my World History classroom, several students were already seated at their desks. Their avatars all sat motionless, with their eyes closed. This was a signal that they were “engaged,” meaning they were currently on phone calls, browsing the Web, or logged into chat rooms. It was poor OASIS etiquette to try to talk to an engaged avatar.They usually just ignored you, and you’d get an automated message telling you to piss off.

I took a seat at my desk and tapped the Engage icon at the edge of my display. My own avatar’s eyes slid shut, but I could still see my surroundings. I tapped another icon, and a large two-dimensional Web browser window appeared, suspended in space directly in front of me. Windows like this one were visible to only my avatar, so no one could read over my shoulder (unless I selected the option to allow it).

School in OASIS bears a marked a resemblance to the traditional classroom. Students attend classes synchronously in the virtual environment. A teacher leads the class in something like a lecture format, but this lecture can be supplemented by virtual materials that would be impossible in a traditional class. For example, students can take a virtual tour of the human body on board a microscopic submarine in Biology. Students have opportunities to interact with each other as well and a “mute user” option makes it possible to avoid virtual bullying.

I think it’s also worth mention that this type of virtual school is quite possible with today’s technology. For example, virtual schools already exist in Second Life.

Common Themes

While this is a small sample of Sci-Fi classrooms, I think there are some patterns here that are worth noting.

Education is an institution of great power

First and foremost, these Sci-Fi stories depict education as a very powerful force in human development. This is something of a double-edged sword. Education can be used as a tool to enlighten individuals or it can be used to preserve a system of authority.

There’s an old maxim stating that “knowledge is power”. Sci-Fi takes this maxim one step further by showing us worlds where restricting access to knowledge can make individuals powerless. As a society, we need to take steps to ensure that information is open and available to avoid falling into a trap of historical revisionism.

Lectures are here to stay

Most of these Sci-Fi classrooms seem to fit the template of the “traditional lecture”. A teacher stands in front of the class and delivers information to the students. Perhaps part of the reason for this is that the “lecture” is so pervasive in our culture that we wouldn’t recognize these as classrooms if they were structured otherwise. Our familiarity with the format means that we quickly recognize the scene as a “school”. This format allows the Sci-Fi plot to make its point and move on in a short amount of time.

Despite the dated classroom format, the technology in the classroom opens up new methods of presenting information. The chalkboards have gone electronic and the Power Point slides have been replaced by holographic projections. The interesting part is that despite all this technology, these Sci-Fi classrooms often still have a human teacher. Computers might be used to disseminate information, but learning is guided by a “real teacher”. This suggests that the role model that teachers provides is an important part of the educational process. The teacher is trusted to make an appropriate use of the technology to engage students in the practice of critical thinking.

School is a social experience

Another related trend in these Sci-Fi classrooms, is that the students gather in the same place at the same time. This suggests that students interacting with each other is an important part of the school experience.

This is particularly curious in the case of Star Trek and makes for an interesting comparison with present day hybrid courses. In a typical hybrid course, students have both asynchronous “homework” time (typically done over the Internet) and synchronous “classroom” time. What’s interesting to me about the Vulcan classroom is that it a synchronous environment with primarily asynchronous instruction. During the instructional time, students interact primarily with the computer rather than each other. It might be comparable with an online class that you were required to take in person.

It may be that the concurrency of having students gathered in a single location is to support the development of social skills, but in the case of several protagonists this has the negative side effect of bullying. Ready Player One solves this bullying issue by transitioning to a fully virtual classroom. Students can simply block electronic messages from others if they choose.

Conclusion

While we obviously don’t want to base educational practices on anecdotes from science fiction, I think that these Sci-Fi stories mirror the struggles of today’s teachers.  On one hand, teachers want to adhere to practices that have worked in the past.  One the other hand, teachers can see the value in exposing students to new technology.   What we see in these Sci-Fi classrooms is the result of both of these influences.  They look like present day classrooms, only the tools have been replaced with the latest hi-tech gadgets.  In effect, the Sci-Fi classroom is generally just a superficial make-over of our existing cultural expectations of school.

Of these Sci-Fi classrooms, the one that gives me the most hope for the future is Voyager.  Naomi’s education is a balanced mixed of numerous sources.  She spends a lot of time learning from holographic children’s programs, but also electronic textbooks, human role models, and hands-on science experiments.   The important point to be made here, is that the new technology adds to the educational experience rather than just replacing existing tools.   The presence of pen and paper note-taking in the Serenity classroom is another telling indicator that good teaching doesn’t necessarily require advanced technology.

As far as the educational technology goes, some of these Sci-Fi devices might not be too far off.   The difficulty is going to be integrating them into the classroom effectively.  It needs to be used in a way that contributes to the learning experience or it runs the risk of becoming a distraction.  In some ways, this is already a issue.  How much lost classroom time do teachers owe to fiddling with projectors, doc cams, and Power Point?  Perhaps the focus of educational technology developers should be on streamlining the existing tools into a seamless classroom experience.  Creating voice controlled lecture tools might provide a nice stepping stone between the classrooms of today and the ones we see in science fiction.   Any technology that frees up a teacher’s time to focus on students’ learning is likely to be a welcome addition to the classroom.

One thing’s for certain, it sure is an exciting time to be a teacher!

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I’ve seen a lot of new mesmers on SoR and occasionally I get questions about gear, traits and general WvW tactics. In an effort to help some of aspiring SoR mesmers out, I decided to put together this mini-guide with some general information about playing a mesmer in WvW. This is not a “here’s Flash’s build, just copy it and pwn face” thread, but rather a look at some of the options you have available to you as a mesmer and how to use your tools most effectively.

I. Weapons

Early on in your Mesmer career, you should be experimenting with the different weapons available to you. Each weapon has different strengths and weaknesses, and the weapons you choose use will have a large impact on how your Mesmer plays. Scepter, Staff and Torch tend to complement a condition damage build. Sword and Greatsword tend to complement a power build. However, any weapon can be used in either if you trait and gear appropriately.

My personal opinion is that Sword and Focus is the way to go for WvW. The focus is clutch in WvW for providing group swiftness, pulling people off of walls and ledges, and negating projectiles. The main reason for using sword is the two seconds of invulnerability with Blurred Frenzy. This can be a real life saver in a pinch. Scepter and Focus can be a decent while leveling up since it allows you to stay out of melee range, but the block on the 2 skill is sub-par in comparison. I use greatsword on my weapon swap for the AoE cripple in open field fights, but switch to a staff in siege situations to AoE up walls. You can run both Greatsword and Staff if you like, but you’ll probably want to use a rune set for swiftness to get around faster.

II. Traits

Your first 5 trait points for any build should go into Illusions. This minor trait is pretty much mandatory for any mesmer, because it reduces the cool-down of all illusion summoning skills by 20%. Since most of your DPS comes from illusions, either directly through phantasms or indirectly through shatters, this is a very effective DPS increase across the board. This trait is arguably too good to pass up considering how few trait points are needed to acquire it. As you continue leveling up to 40, your next points should go into Dueling and Domination for the stat increases because you don’t really have many options for condition damage at that level.

At level 40 the whole game changes because you gain access to the 2nd tier of traits. Putting 20 points into Dueling is almost mandatory. Choose II and X as the Majors. Together, these traits give you vigor on crit, fury on phantasms, bleeding on illusion crits, and clones on dodge. The reason I say that these are almost mandatory is the “clone on dodge” trait. This is both an offensive tool and a defensive tool that will significantly alter how you play. For the first time, you’ll actually generate illusions at a fast enough rate to make full use of your shatter skills.

A lot of PvE mesmers avoiding using shatter skills because keeping up 3 phantasms can output a significant amount of damage. In WvW, this doesn’t work because your phantasms simply will not live long enough. Instead, you should allow your phantasm to execute its first attack and then shatter it to add AoE damage on top of it. You can also use your shatters defensively. A dodge or two followed by Diversion or Distortion can buy you a few seconds to escape, which can mean the difference between life and death in WvW. The vigor on crit trait makes sure you have a steady supply of endurance to keep dodging with.

In addition to Deceptive Evasion, the 15pt minor makes your illusions inflict bleeding on critical. This trait is essential because it makes your previously damage-less clones actually put pressure on the opponent. This trait is a solid 10%-20% DPS increase even if you don’t spec for condition damage. If you are speccing for condition damage, this trait is essential for stacking bleeds on your opponent with weapons that otherwise would not have condition damage on them.

Once you’ve filled out the essential 0/20/0/0/5 traits, the rest of your traits are really up to you. Take a look at the major traits in tiers 2 and 3 and see what interests you. I’ll cover some of the more common variants that you’ll see in WvW.

20 in Domination: The notable major here is Shattered Concentration which makes your shatter skills strip boons. This is a highly valuable thing to in the current meta where zergs stack and buff up before charging into fights. The minor traits adding vulnerability are a nice bonus. Condition builds might also like Confusing Enchantments which causes confusion to foes that enter or exit glamours. This works well because people have a natural tendency to move out of red circles.

30 in Dueling: Empowering Mantras can provide a nice passive damage bonus for each prepped mantras. I’m not a big fan of the mantra play style, but it’s a common variant that’s worth mentioning.

20 in Chaos: Going 20 points into Chaos can give you “Descent into Madness” and “Mirror of Anguish”. The former reduces fall damage by 50% while the latter will apply crowd control effects to the person that used it on you. Both of these traits together give you a big advantage on high terrain.

20 in Inspiration: The notable WvW trait in the Inspiration is Warden’s Feedback. This makes your focus skills reflect projectiles. A very significant amount of the damage in WvW is projectile based and this trait turns Temporal Curtain into a valuable tool for both offense and defense.

30 in Illusions: The big trait in this tree is Illusionary Persona. This trait adds a shatter effect on you in addition to your illusions. This adds extra punch to your shatters when in melee range, but the big bonus is that it allows you to use your shatter skills without any illusions at all! Being able to use Distortion with no illusions for 1 second of invulnerability can save your life if you get hit by a backstab thief or bull rush warrior. Add Illusionary Invigoration and you get two extra lives. Fair warning: once you try IP it’s hard to go back to life without it. Another common variation for condition builds is to take both Dazzling Glamours and Blinding Befuddlement, which make glamours cause blind and confusion. The 15pt minor adding confusion to all shatters is also a must for condition builds.

Remember that you can always change major skills when out of combat. Keep this in mind when creating your build so that you can adapt to different situations. For example, I like to switch between Mender’s Purity and Glamour Mastery in Inspiration depending on whether or not I have Null Field equipped so that I always have some form on condition removal.

III. Stats and Gearing

First and foremost, you goal with gearing should be to stay alive. This means you should be stacking toughness and vitality until you stop dying, and then start focusing on increasing your DPS. For a power build, I’d suggest about a 50/50 mix of Soldier’s gear (Power/Toughness/Vitality) and Berserker (Power/Precision/Crit Damage). For a condition build, Rabid (Condition Damage/Precision/Toughness) is the way to go, perhaps with a bit of Carrion (Power/Vitality/Condition Damage) to increase your HP and help against siege. While the options are limited, gear with “+ to all stats” can be effective in either case.

My personal preference is with the power oriented gear. Condition mesmers can be quite deadly in WvW against players, but conditions do not effect siege weapons and taking down siege weapons quickly is very important in WvW. If you want go the condition route you might want to lean more towards a hybrid spec using Rampager’s (Precision/Power/Condition Damage).
There’s something of a sweet spot with vitality and toughness that will maximize your “effective health”. Take your total armor (base+toughness) and multiply it by 10. If the result is less than your total HP, then you need more toughness. If the result is greater than your total HP, then you need more vitality. At your discretion, you can run healing power instead of vitality but I wouldn’t really recommend it outside of some very specific support builds.

Keep in mind that your illusions only benefit from Power, Precision, Critical Damage, Condition Damage, and Toughness. Your illusions have fixed health regardless of your Vitality and the boons and conditions they apply will not be extended by boon or condition duration bonuses. If you find your illusions are dying before they reach their targets, you might want to add more Toughness.

IV. Sigils

If you’ve followed my advice so far, then you probably have a high enough critical rate to open up a variety of options for Sigils. In particular, Sigil of Earth allows you apply bleeds with weapons that ordinarily would not apply conditions (i.e. Sword) and is essential if you plan on going with a condition/hybrid spec. Sigil of Earth is still good in a power build, but Strength, Blood, Air, Fire, Force and Accuracy are all good options as well. Obviously you’d want Bloodlust or Corruption on at least one of your weapons as well, and you can always switch weapons later and keep the stacks. Sigil of Energy is another common option, as the extra endurance will help keep you alive and can also be used offensively to create more clones.

V. Runes

There are a number of viable options for Runes as well, depending on what you need to complement your build. Air and Centaur runes are commonly used for the swiftness on heal effect because mobility is very important in WvW. Scholar runes are probably the best option for increasing your damage, but Ruby orbs can be a cost efficient alternative. Divinity runes would probably work well regardless of your spec, as you benefit from all the stats provided, but are pretty expensive also. Infiltrator runes are nice and affordable option because the stealth effect at 10% health will cause your opponent to lose target on you and have to pick you out from your clones again. Undead is a nice option for condition builds as it complements the 25pt Chaos trait nicely. Melandru runes could be helpful if you find yourself struggling against crowd control effects. Remember that you can always experiment with various other options in sPvP without spending any gold.

VI. Food Buffs

My personal favorite food buff is the Omnomberry Pie. Regardless of whether you’re a power or condition build, you benefit from the bonus to precision. The life steal on crit will contribute to both damage and healing at the same time. Foods that reduce stun or condition duration are also a good choice. You can also use generic Power or Condition Damage food depending on your spec.

At some point you should make a trip to Wayfarer Foothills to buy the animal spirit offerings from the heart venders. Head to the Iron Marshes and pick up the Scale Venom from the escort event in the south eastern part of the map (Edit: Scale Venom is slated to be removed from WvW in the next patch). These bonuses are very small, but you might as well take advantage of them while they still can be used in WvW.

Edit: Kaska drew my attention to Orrian Truffle and Meat Stew, which gives Might on Dodge and +40% Endurance Regen. This is another nice alternative that will add to both your damage (more dodges = more clones) and survival.

V. Skills

Healing Skills
You’ve got three options for healing. Ether Feast is the simplest to use, but often times you’ll need your heal the most when you don’t have any illusions up and will miss out on the bonus healing. Mantra of Recovery is actually the best healing-per-second Mesmer skill (even untraited), but takes some getting used to because you need to prep it in advance. MoR is also unique in that it can be used while stunned or knocked down. Mirror is my personal favorite, but in order to get the most of it you need to be proactive about reflecting projectiles. MoR and Mirror both synergize nicely with “on heal” effects from runes or traits because of the low cool-downs. I’d recommend that you start out using Ether Feast and transition to Mirror or MoR later depending on your play-style.

Utility Skills
The utility skills are where mesmer really shines. Here are some of the more important WvW ones ordered by tier:

Tier 1
Blink – This one never leaves my bar. It breaks stuns and teleports you to the target location.
Decoy – Breaks stun, summons a clone and provides 3s of stealth. It’s an all-around great skill.
Null Field – Removes boons from foes, conditions from allies, and provides an ethereal combo field. It seems to affects 5 enemies and 5 allies with each pulse (though not necessarily the same ones).

Tier 2
Feedback – Creates a bubble that reflects projectiles. Centered on target if you have one, or ground targeted otherwise. Use it on your gate while defending and watch the damage numbers fly. It counts as an ethereal field and reflected projectiles count as a finisher, so they have a chance to apply confusion also. It doesn’t appear to have a target cap.
Mirror Images – Breaks stun and summons 2 clones. Use this between two quick shatters for some nice spike damage.

Tier 3
Portal Entre/Exeunt – Used to move groups of people from one location to another, particularly golems. Note that it is limited to about radar range and provides no indicator if you exceed the max. Learn to judge the distance well so that it doesn’t fizzle. I cover more on portal tactics later. The portal is limited to 20 uses.
Veil – Provides allies crossing it with 4s of stealth. Use it to hide your group’s initial melee rush or to make an escape from combat. It doesn’t appear to have a target cap. The tool tip for this skill incorrectly lists it as a light field, when in fact it functions as an ethereal field.
Mimic – A pretty sub-par skill compared to Feedback, but it’s worth mentioning here because it can absorb ballista shots. You’ll only use this skill in situations where you’re trying to protect siege from ballista fire.
Mantra of Concentration – Again, not a great skill overall, but it’s a mesmer’s only source of stability and there might be situations where you need it.

Elite Skills
Time Warp – Easily the best mesmer elite. Use this on melee during a rush or on golems. Has a 5 target cap.
Moa Morph – Not worth it in WvW at all because 1 on 1 situations are so rare. Only unlock it to move to next tier.
Mass Invisibility – It’s worth unlocking, but very situational. Equip it when you’re solo (either roaming or hiding) so that you can avoid unnecessary confrontations. Note that this skill is limited to 10 targets.

VI. General Game-play

Mesmer is kind of a unique class. None of the skills do exceptionally high damage on their own like a Warrior’s Killshot or Thief’s Backstab. Instead, the mesmer’s specialty is dealing moderate damage from multiple sources simultaneously. Your goal is stack as many skills as you can into as small of time frame as you can. You can potentially hit with a phantasm, a direct damage skill, a shatter skill, and a utility skill all at the same time. This can add up to large “spikes” of damage, but requires that you do a lot of planning in advance to set it up. However, the end result can be quite deadly when you pull it off.

Since my preferred weapon combination is sword/focus, I’ll use that as an example to illustrate the concept. Here, we’ll use Mirror Images as a utility skill and Deceptive Evasion/Illusionary Persona as traits. I open with Illusionary Leap, which spawns a clone that leaps to the foe and cripples them. I follow this with iWarden, and immediately after it finishes casting hit Swap. This immobilizes the foe next to the Warden and teleports me into melee range. While the Warden is wailing on them, I supplement this with Blurred Frenzy. Once the Blurred Frenzy finishes, I dodge forward to generate my third clone, shatter with Mind Wrack, follow with Mirror Images and a dodge back for 3 more clones, and finally shatter with Cry of Frustration. This is more than enough to down glass cannons in about 3 seconds, and any opponents that do survive are left with 12 stacks of confusion and about 4-5 stacks of bleeding.

With a condition mesmer, the same concepts still apply but the set-up is a little more complicated. The basic idea is to continually spawn clones to apply bleeding (and burning in the case of staff) to your opponent to gradually work their health down over time. While doing this, you want to pay close attention to that opponent’s behavior. You want to be able to predict when they’re about to attack and hit them with Cry of Frustration. The goal here is to create a “damned if you do, damned if you don’t situation”. The opponent can try to kill you and eat the confusion damage, or they can stop attacking and sit there while the bleeds tick away at their health. Most of your damage as a condition mesmer is going to come from confusion, so you want to time your skills to put as many stacks of it on them while they are attacking. If you combine shatters, phantasms, direct skills, and utilize your ethereal fields creatively, it’s quite possible to put up to 25 stacks of confusion on an opponent by yourself for a short period of time. Another good tactic to use is to stun or daze your opponent before you start stacking confusion. People have a natural tendency to use skills immediately after their skills become available again.

VII. Fun with Portals

Mesmers are uniquely valuable in WvW for their ability to teleport groups across large distances very quickly using Portal Entre/Exeunt. Here are some situations where you might use portals to great benefit:

Supply Runs – Running supply is a good place to practice judging the portal placement range because it’s a very low risk situation. Place your portal outside the supply camp, run in to pick up supply, then portal back to your original location. One very special situation to use this is at the north-west tower in the borderlands. If you place a Portal Entre at the very back of the lord’s room and place the Exeunt near the base of the cliff at the supply camp, you can teleport all the way back into the tower! Because of the large elevation difference between the tower and supply camp, this can save a substantial amount of travel time and allows you to avoid the front entrance if it’s under attack.

Escape Portals – Having a Portal Entre placed before engaging enemies can provide you with a nice safety net if things go bad. This is especially useful when defending keeps or towers because it allows you to safely stand on the wall without fear of being pulled off. If you’re on teamspeak, as you should be, call out “escape portal” so that they know it will take them to safety as well.

Retreat Portals – Sometimes it’s helpful for you to support a group retreat by placing your Entre near your commander, running away from the enemy forces, and then dropping the Exeunt. Try to give your allies a few seconds notice before dropping the Exeunt so that they can start heading towards the Entre before it opens. If your commander wants to reengage afterwards, drop a Veil to stealth your group to make it look like you’ve ported out.

Feigned Retreat Portals – The basic idea behind this portal is that you place the Entre in an inconspicuous location and retreat as a group. When the enemy forces chase your retreating group past the portal, you open the Exeunt and teleport your group behind them to hit the backline. This tactic is a high risk maneuver because if the enemy spots your Entre on the group they may focus AoEs on your group when it becomes active. Try to use the terrain to place your Entre out of sight to avoid this situation. If you think your portal has been spotted, warn your group not to take it and open the portal anyway. This may cause the enemy to blow their cool-downs on the portal and give your group an opportunity to push from the front.

Offensive Portals – The offensive portal is often the hardest to pull off but also the most useful. A well placed offensive portal can allow you to flank enemy forces or take out hard to reach siege weapons. I’d highly recommend that you break command before attempting this tactic so you can adjust your skill set. I typically use Mirror, Blink, Decoy or Veil, Portal, and Mass Invisibility for this situation. Open with Temporal Curtain to give yourself swiftness and follow with Mass Invisibility for 5 seconds of stealth. Pay close attention to the red circles on the ground and blink past or dodge roll through them. When your stealth fades, you can use Decoy or Veil to provide you with a few more seconds. Keep in mind that your blink is most effective when used to teleport to higher ground. In particular, you can teleport to the ramp leading to the 3rd floor of Garrison in borderlands by targeting the underside of the geometry. If you’re spotted, use Mirror to reflect incoming projects for an extra second of protection because the last thing you want in this situation is to be crippled, chilled or immobilized!

Ninja Portals – This type of portal is used to take groups past the wall of a keep or tower that you previously had access to, allowing your group to recap it later. Spend a few minutes in each tower and keep to look for hiding spots. Follow around a more experienced player on a mesmer sweep to learn some of the common locations. Equip your stealth skills to buy you some extra camouflage. If the enemy is thorough with their sweeps, you’re probably going to get found regardless of where you hide. If this happens, ask if there are any thieves in the tower/keep before releasing as you might be able to get a res. Learn the safe spots where you can jump down form each keep/tower so that you don’t die from fall damage.

Portal Chains – The last type of portal requires multiple mesmers. This is mainly used to transport golems over large distances. It helps to form an all-mesmer group to pull this off. First decide on an order. Alt click the minimap in the direction you’d like to travel to place a personal waypoint. This serves as a marker for where the next mesmer should start. Once all your waypoints are placed, call “drop and go” in TS. Place the first portal and run toward your waypoint. You need to stagger your portals by a few seconds to give the golems time to move into position, and call “1st”, “2nd”, etc. so that the other mesmer know when to drop their exits. It’s important that you do not overlap portals either, as it makes it difficult to get the interaction prompt. Typically its easiest if you Time Warp the golems in the same order as you ported them. It also helps if the mesmer who drops the first portal is spec’d for Glamour Mastery so that it comes off cool-down in time to provide an escape portal if necessary.

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I know it doesn’t seem like a big deal, but it took a long time for me to feel comfortable with those words.

When I started this blog three years ago, I wasn’t really sure where I was going with it. I started it in conjunction with my “experiment” of joining Twitter, as a place for me to expand on ideas beyond the 140 character limit. However, I was hesitant to reveal my real identity on either.

The reason for this is because I’m a teacher. I teach developmental mathematics at a local community college. Considering the substance of my Twitter feed, this probably isn’t a huge surprise. However, I’ve heard horror stories of teachers getting in trouble for things they’ve said on social media sites. Since I had know idea what I would be saying, I did the sensible thing and adopted a pseudonym.

Operating under pseudo-anonymity gave me a sense of freedom. I felt comfortable talking about topics like religion and politics that are considered a classroom taboo. I knew that anyone who really wanted to find out my identity could; it just probably wouldn’t have been worth the effort. I could always fall back to the disclaimer on the right that “the comments on this blog are my own and may not reflect the opinions of my employer”, but the lines regarding such publicly made comments are fuzzy at best. Nonetheless, I have opinions and I don’t feel like I should need to hide them. I consider most of them to be well thought out and all of them are subject to change with sufficient evidence.

So why the sudden change of heart?

Well, it wasn’t really so sudden…

When I first started this experiment, developed something of a persona for Suburban Lion. Whereas I was fairly introverted and hesitant, Suburban Lion was extroverted and impulsive. While the real me would bite my tongue to avoid hurting someone’s feelings, Suburban Lion would speak his mind openly and publicly. This internal struggle is well captured by the symbolism of my chosen alias. I was like a house cat who fashioned himself king of the jungle.

As my social media endeavor progressed, a couple things happened.

First, it’s become increasingly difficult to keep my real identity a “secret”. I knew from the start that my online interactions would never be completely anonymous, but the more information I posted online the more I realized how futile the effort was. Not to mention the fact that I’ve been signing all my code with my real name this whole time for copyright reasons.

Second, I feel like I have a better idea of the direction this blog is going. At a glance, it might seem to be an eclectic mix of politics, video games, and education. It’s the mathematics tying these remote topics together that’s piques my interest, and provides the common thread of this blog. I’ve also come to the realization that it’s the act of blogging that I enjoy. I will continue to blog on things that I find interesting. If people enjoy reading those thoughts, that’s great! If not, that’s fine also. The learning experience that I’ve gained from communicating with others through this blog has been rewarding enough on its own.

Finally, and perhaps most significantly, I feel like the distance between my real identity and my online persona is narrowing. Suburban Lion has become a little more reserved and a little less argumentative. On the other hand, the “real me” has become a little more sociable and assertive. It’s gotten to the point where the differences between Ryan and Lion have almost disappeared. “Almost” being the operative word.

Where do we go from here?

My goal with this is primarily for personal growth. By tearing down the wall separating my online identity and my real identity, I feel more motivated to live up the ideals that “Suburban Lion” personifies to me. At the same time, I hope that this move breathes new life into “Suburban Lion” by putting a name to the face behind the screen.

It’s not just about the name either, but an identity. There are a lot of Ryan Ruffs out there, but only one Suburban Lion. Well, it turns out that there are actual suburban lions, but that’s beside the point. I’ve been interacting online since I was a teenager. It’s time that I started to connect these interactions to a central point. It probably won’t happen overnight, but I’ve got to start somewhere.

Special Thanks

I’d like to thank the community on Twitter for making this possible. Thank you for setting a good example of how to develop my “Personal Learning Network”. Thank you for never holding my pseudo-anonymity against me and judging me primarily on the contents of my tweets.

I’m sorry it took this long for me to come clean, but maybe something good will come out of it. I’m sure that there are many others on Twitter going through the same anonymity dilemma as I did. Perhaps this post will provide them with some digital courage.

Thanks for reading!

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Hello! My name’s Ryan and I’m an “undecided” voter.

No, it’s not what you think.

I’m not undecided between these guys:

Obama Romney

There’s no way in hell I’m voting for Romney.

I’m not an idiot as Bill Maher not-so-subtly suggested last week. (It’s okay Bill, I can take a joke)

I’m undecided between these guys (and gal):

Obama Johnson Stein

Mathematician and author John Allen Paulos described the situation a little more elegantly:

I’d like to believe that I fall into the “unusually thoughtful” category and wanted to share my perspective.

FULL DISCLOSURE: This is my personal blog and obviously biased by my opinions. I’m a member of the Green Party and have made a “small value” donation to the Stein campaign. Despite my party membership, I try to vote based on the issues and not the party. I voted for Obama in 2008 and voted for Ron Paul in the 2012 GOP primary. While I’m not technically an “independent” due to my affiliation with the Greens, I’m probably about as close to one as it gets.

Let’s start with a little historical background and work our way forward from there.

The Nader Effect

My first voting experience was in the 2000 election. I didn’t like either Gore or Bush, and ended up gravitating towards the Nader campaign. His positions on the issues most closely aligned with my own, so I did what seemed like the most rational thing to do at the time. I voted for him.

After the election, Nader (and the Green Party in general) received a large amount of criticism from Democrats for “spoiling” the election. The Democrats argued that votes cast for Nader in key states like Florida, would have been otherwise been cast for Gore. The counter argument is that Bush v. Gore was decided by the Supreme Court, but I won’t get into that.

From my perspective, my vote for Nader in this election could not be counted as a “spoiler”. I was living in California at the time, and the odds of California’s votes in the Electoral College going to Bush in the 2000 were negligible. My vote for Nader was completely “safe” and allowed me to voice my opinion about the issues I cared about. However, this notion of a “spoiler vote” forever changed how I thought about my voting strategy.

Independence of Irrelevant Alternatives

In the 1950s, economist Kenneth Arrow conducted a mathematical analysis of several voting systems. The result, now known as Arrow’s Impossibility Theorem, proved that there was not ranked voting system that could satisfy the following conditions for a “fair” election system:

  1. It accounts for the preferences of multiple voters, rather than a single individual
  2. It accounts for all preferences among all voters
  3. Adding additional choices should not affect the outcome
  4. An individual should never hurt the chances of an outcome by rating it higher
  5. Every possible societal preference should be achievable by some combination of individual votes
  6. If every individual prefers a certain option, the overall result should reflect this

Arrow was largely concerned with ranked voting systems, such as Instant Run-off Voting, and proved that no such ranking system could ever satisfy all of these conditions. There are non-ranked voting systems that meet most of these conditions, such as score voting, but one of these conditions of interest that our present system doesn’t meet is number 3. This condition goes by the technical name of Independence of irrelevant alternatives. The idea is that the outcome of a vote should not be affected by the inclusion of additional candidates. In other words, there should never be a “spoiler effect”.

What I find interesting here is that the very mechanics of our voting system lead to a situation where the outcome of elections is controlled by a two party system. It forces citizen to vote tactically for the “lesser of two evils”, while from my perspective both of those “evils” have gotten progressively worse. George Washington warned of this outcome in his farewell address:

However [political parties] may now and then answer popular ends, they are likely in the course of time and things, to become potent engines, by which cunning, ambitious, and unprincipled men will be enabled to subvert the power of the people and to usurp for themselves the reins of government, destroying afterwards the very engines which have lifted them to unjust dominion.

Until we can address the issues inherent in our voting system itself, I’m left with no choice but to vote strategically in the election. My policy for voting is a tactic of minimaxing: minimizing the potential harm while maximizing the potential gain. It’s with this strategy in mind that I turn to the options of the 2012 presidential race.

Quantifying Politics

In order to apply a mathematical analysis to voting, it is first necessary to have some way of quantifying political preferences. As a method of during so, I’ll turn to the so called Nolan Chart. An easy way to find out where you stand on the Nolan Chart is the World’s Smallest Political Quiz. Here’s where it places me:

Here’s where I’d place the 2012 candidates:

Note that this is my subjective opinion and may not necessarily reflect the opinions of the candidates themselves. It’s also important to note that this is a simplified model of political disposition. There are other models, such as the Vosem (восемь) Chart that include more than two axes. If you were, for example, include “ecology” as a third axis, this would place me closer to Stein than Obama and closer to Obama than Johnson. The resulting distances to each are going to vary depending on what axes you choose, so I’m just going to stick with the more familiar Nolan Chart.

Since I’m politically equidistant from each of the candidates, my minimax voting strategy would suggest that I vote for the candidate that has the highest chance of winning: Obama. However, there are many more variables to consider that might result in a different outcome. One of those variables is something I call “political flux”.

Political Flux

People change. It’s a well known fact of life. Changes in political opinions are no exception. If you look at the stances that Obama and Romney have made during this campaign, and compare those to their previous positions, I think you’ll see a trend that looks something like this:

Obama campaigned hard left in 2008, but during his term in office his policies have shifted more towards the center. Romney campaigned in the center while he was running for governor of Massachusetts, but has shifted more towards the right during his presidential campaign. These changes are highly concerning to me, because both candidates are shifting away from my position. Thus, while Obama is closer to me on the political spectrum, the fact that he is moving away from my position makes the long term pay-offs lower than they would be if he had “stuck to his guns”. In turn, this makes the 3rd party candidates a more appealing option.

I might even go so far as to suggest that this “political flux” is the reason why these 3rd party candidates are running. Statistically, their odds of winning are too low to change the outcome of the election. However, they can influence the direction of the political discourse. The more people that vote for those candidates, the more likely that future candidates venture in those respective directions. This vote comes at a “risk” though, as those 3rd party candidates run the risk of “spoiling” the election for a less undesirable candidate. The level of this this risk varies from state to state due to the electoral college system.

The Electoral College

A popular vote is not enough to win the election. The president is selected by an Electoral College that gets a number of votes based on a (mostly) population proportional system. For some of these states, the polls predict a pretty solid winner and loser for the presidential race. For others, the state has a tendency to lean right or left. According to The New York Times, the following states are considered a “toss-up” in the upcoming election:

  • Colorado
  • Florida
  • Iowa
  • North Carolina
  • New Hampshire
  • Nevada
  • Ohio
  • Virginia
  • Wisconsin

If you are living in one of these states, the risks of voting for a third party are greater because your vote will have a higher chance of “spoiling” the election for one of the candidates. I happen to live in Virginia — one of the 2012 “battleground” states. I foresee a large number of attack ads in my near future. The big question is, is the pay-off worth the risk?

Aikido Interlude

For the past couple months, I’ve been studying Aikido — a martial art that might be best described as “the way of combining forces”. The idea is to blend ones movements with those of the attacker to redirect the motion of the combined system in a way that neither individual is harmed by the result. As a lowly gokyu, I still have a lot to learn about this art, but I find some of the core principals behind it rather insightful from a physical and mathematical perspective.

The basic idea is a matter of physics. If an object has a significant amount of momentum, then it takes an equal amount of momentum to stop it. However, if you apply a force that is orthogonal (perpendicular) to the direction of motion, then its relatively easy to change the direction of motion. You don’t block the attack in aikido. You redirect the attack in a way that’s advantageous to your situation. You can see the basic idea in my crude drawing below:

The result of this is that many aikido techniques end up having a “circular” sort of appearance. In reality, it’s the combination of the attacker’s momentum and the orthogonal force applied by the defender that cause this. See if you can spot this in the following video of Yamada sensei:

So what does this have to do with voting?

Well consider my position on the Nolan Chart and the direction that the two major candidates are moving in. As much as I would like to shift the debate to the left, it would require a significant amount of political force and time to negate this momentum towards the right and even longer to push it in the opposite direction. It would be much more efficient to push “north” and allow the momentum to carry the political culture towards my general position.

In other words, voting for Gary Johnson might actually be the path of least resistance to my desired policies.

Metagaming the Election

Here you can start to see my predicament. Part of me wants to vote for Gary Johnson, because I think that doing so would be mostly likely to shift the debate in the direction I want it to go. Part of me wants to vote for Jill Stein, as doing so would help strengthen the political party that I belong to. Part of me wants to vote for Barack Obama, but only because doing so would have the greatest chance of preventing a Romney presidency. According to the latest polling data, the odds of Obama being re-elected are 4:1. Those are pretty good odds, but this is a high stakes game. It sure would be nice if there was a way to “have my cake and eat it too”.

It turns out that there is.

I can metagame the election.

The idea of metagaming, is that it’s possible to apply knowledge from “outside the game” to alter one’s strategy in a way that increases the chance of success. In this case, I’ve decided to employ a strategy of vote pairing.

You see, I live in the same state as my in-laws who traditionally vote Republican. However, despite a history of voting GOP, they’re both very rational people. Romney keeps shooting himself in the foot by saying things that are downright stupid. Screen windows are airplanes? Free health care at the emergency room? The more Romney talks, the easier it becomes to convince rational people that he’s unfit to be president.

After many nights of debate, we’ve come to the realization that we’re only voting for one of the two major parties because the other party is “worse”. From there, a solution presents itself: “I’ll agree to not vote for Barack Obama if you agree to not vote for Mitt Romney”. This agreement is mutually beneficial to both parties involved. Without this agreement, our votes just cancel each other out. With the agreement, the net benefit to each candidate is still zero but now those votes are free to be spent elsewhere. The end result is that we each have a larger impact on the presidential election without altering the outcome.

With the vote pairing secured, I’m free to vote for Stein or Johnson at my own discretion. Both of these candidates agree on what I think is the most important issue: ending our “wars” (of which there are too many to list). They differ on a number of issues, particularly on economics and the environment. Personally, I think that the Greens and Libertarians need to meet half-way on the issues for an Eco-libertarian ticket. Jill Stein needs to recognize that the US Tax Code is a mess and needs reform. Doing so can help eliminate corporate handouts, many of which go to industries that adversely affect public health. Gary Johnson needs to recognize that laissez-faire economic policies alone will not fix our broken health care system or halt the impending climate change. I’m going to be looking forward to seeing debates between Stein and Johnson which I think will highlight the complexities of these issues and hopefully identify some possible solutions.

That’s great, but what can I do?

You can enter a vote pairing agreement with someone of the opposite party. If you would ordinarily vote for the Democrats, you can click here to find out which of your Facebook friends “like” Mitt Romney. If you would ordinarily vote for the Republicans, you can click here to find out which of your Facebook friends “like” Barack Obama. Talk about the issues that are important to you in the race, discuss your objections to the other candidate, and if things go well, agree to both vote for a third party. If everyone did this, one of those 3rd parties might actually win. Even if it doesn’t change the outcome, you’ll know that your vote didn’t “spoil” the election for your second choice.

If you want to go one step further, you can Occupy the CPD. Sign the petition to tell the Commission on Presidential Debates that you think we should hear from all qualified candidates and not just the two that they think we should hear from.

Finally, research the alternative parties and join one that matches your personal beliefs. Even you end up voting for one of the two major parties, joining a 3rd party and supporting that movement can have a significant effect on future campaigns. Here’s a few links to get you started:

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When I first played the original Guild Wars beta, over 7 years ago, the mesmer came with a disclaimer on the character creator stating that the profession required advanced tactics and may not be suitable for new players. I was hooked on the mesmer from there on. In Guild Wars 2, this iconic class has undergone a substancial overhaul and is much more self-sufficient than in the original. However, the GW2 mesmer still has a somewhat steeper learning curve relative to some other professions. I posted a version of the following on the official forums during BWE3 to help new players more effectively use the mesmer’s starting weapon: the scepter. My hope is that this guide will help make the first 10 levels of the game as painless as possible, at which point you can really start to customize the mesmer to your preferred playstyle.

Every new character in GW2 starts in a story mode instance based on the selected race. If this is your first time playing GW2, you should use this opportunity to check out the game options, display settings and key bindings before heading off towards the opening quest objective. Soon enough you’ll encounter your first enemy or “mob”. You only have one attack unlocked, Ether Bolt, so use it. The basic auto-attack on the scepter has a 3 step chain. On every third attack, it creates a clone that looks like you and attacks your mob but doesn’t really do any damage. Now that you have a clone, let’s use F1 or F2 to shatter him for some extra damage. If the mob is attacking your clone or not attacking at all, hit F1 for Mind Wrack which deals direct damage to the mob. If the mob is attacking you or an ally, use F2 for Cry of Frustration which causes a condition called confusion that causes damage when that mob uses a skill. Try both of them out and get a feel for how much damage they do with a single clone. When you unlock your second skill, Illusionary Counter, you can use it to block an attack and generate a clone or tap it twice to blind your foe instead. Test out both of your shatters with two clones and see how they’ve improved. If you find yourself taking too much damage, use skill #6 to heal yourself. You may even unlock your third weapon skill which is a hard hitting channelled attack that applies several stacks of confusion.

Eventually you’ll get to an epic cinematic and huge boss mob. Look out for red circles or big attack animations and dodge out of the way. If you happen to get hit, don’t panic — you’re not dead yet. Start to use the #1 attack in the downed state on one of the low level mobs in the area. You can also use the #2 skill to create a decoy, the #3 skill to summon a phantasm to lay some extra hurt your target, or the #4 skill to heal yourself if you’re close to bleeding out. Keep it up until you score a kill and rally. Go back to working on the boss mob until you finish it off and save the day!

After killing the boss, you get another nice cut scene and a quest reward. This includes a bag, some XP, some coin, and your choice of two off-hand weapons. I’d highly recommend choosing the focus from the first quest reward. Not only is Temporal Curtain great for travelling, but it’s also great for snaring melee attackers so you avoid getting hit and acts as a light field. The Illusionary Warden gives you some AoE damage — which the scepter is lacking, provides defense against projectiles and doubles as a whirl finisher. This means that once you’ve unlocked both of the focus skills you can do your own skill combos! Start with using Illusionary Warden on a mob then place a Temporal Curtain on top of him. The resulting combo shoots Cleansing Bolts in different directions and remove conditions from allies that they hit. While testing this out, you may observe that the Illusionary Warden is a stationary phantasm, and won’t move until you use a shatter skill. I’d also recommend that you have at least one clone up before summoning the Warden so he doesn’t get killed right away.

Against melee attackers, you want to open with the scepter auto attack and use Temporal Curtain to cripple them. Your goal is to get at least two clones up before the mob gets close to you. When the mob starts to get close, use Confusion Images. While channeling, use Cry of Frustration. Depending on how many clones you had up, the mob should have 8-9 stacks of confusion. and should be just about to swing at you. Use Illusionary Counter to block the attack, and watch the mob take massive confusion damage while you get away scratch free! If that didn’t kill it, go back to auto-attacking, use the dodge roll to avoid the next two attacks, then use Mind Wrack when you get enough clones.

In dynamic events with lots of people, don’t be stingy with your shatters. The odds of you getting 3 illusions up in such a situation are pretty slim unless you’re fighting a champion, so don’t hestitate to do a single illusion shatter if that’s all you can get off before the mob dies. If possible, try to summon your Warden on a target in the middle of a group with high health, let him do his attack once, then shatter him. He’s going to die when your target dies anyways, so you may as well get the most out of it.

Once you’ve reached level 5, you’ll unlock your first utility skill. There’s a lot of really great skills to choose from here, but the one I would recommend picking up first is Blink. This is a ground targeted skill that teleports you to the selected location while breaking stuns. The reason I suggest this skill first is that it will help you get around the map a little bit faster when out of combat, while also helping you keep your distance from melee mobs. Look for skill challenges on the map, marked with the blue chevron, and complete them to unlock some other utility skills of your choice. My personal favorites on the 1st tier are Null Field and Signet of Domination. If you’re unsure of how a particular skill works, you can always use the PvP menu to go to the Mists and test it out on the target dummies there.

Eventually you’ll start to encounter some ranged attackers. Against these mobs you can open with Confusing Images and Illusionary Counter since they’ll generally start attacking right away. Since you get a clone on counter, this will give you a distraction to summon an Illusionary Warden on them and block their projectiles. Once you get a few more skill points, you can combine confusion with the Feedback utility skill to quickly take down ranged attackers.

I’d recommend sticking with scepter/focus until at least level 7 when you unlock weapon swapping. Weapon swapping really opens up a lot of play-style options for the mesmer. It’s much easier to survive as sword mesmer when you can weapon swap to a staff for Phase Retreat after blowing your defensive cool-downs. Likewise, the greatsword benefits from a weapon swap once enemies get close. You may want to keep the scepter/focus on a weapon swap until you unlock all the skills on your weapon of choice. These are just my opinions of course, so if there’s a weapon combination you really want to play with go right ahead! Regardless of what you choose, you should always keep a focus in your bag so that you can switch to it when you’re not in combat for the swiftness buff.

I just hope that these tips help some newcomers who might be turned off by the scepter after hearing horror stories from the first two BWEs. The scepter was vastly improved in BWE3 and I expect it to be even more polished by release. Overall, I think that using the scepter/focus will help you learn how to effectively utilize the core mesmer mechanics. There’s a lot to learn about playing a mesmer, but the class has a nice rhythm once you get used to it. Stick it out for a while and you might be pleasantly surprised!

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This weekend marks the 3rd Beta World Event for Guild Wars 2. I wrote a little bit about my general experiences in the first BWE, but this time I’m focusing on a very specific area of the game. In the first BWE, I was just playing the game and having fun with it. In the second BWE, I started to do a lot more “testing”. In particular, one of the things I was testing was the “Sharper Images” trait.

Sharper Images (SI) is a Dueling trait that causes critical hits from Illusions to inflict bleeding for 5 seconds. This trait was bugged in the first BW1 and didn’t work at all. In the second BWE1, it worked as described but a second phantasm trait called “Phantasmal Haste” was bugged resulting in some crazy damage output. This means that I didn’t get a very good perspective on how these two traits would work together, but that’s okay because I can do the math! In addition to seeing how the phantasm related traits would interact together, I also wanted to find out which stats to gear for in order to maximize my damage. In order to do this, we first need some information about how damage is calculated in GW2. Assuming a level 80 character:

  • Pandara_RA! at Team Legacy worked out the following formula for the base damage of an attack: $$ Base Damage = \frac{(Power) \cdot (Weapon Damage) \cdot (Skill Coefficient)}{Target Armor} $$
  • The chance of getting a critical attack is determined by the Precision above the base: $$ CritRate= \frac{4 + (Precision – Base)/21}{100} $$
  • When an attack criticals, it hits for 50% more damage plus any bonus to critical damage (Prowess). With this, we can find out the average damage of an attack using: $$ Direct Damage = (Base Damage) \cdot (1+(Crit Rate) \cdot (0.5+\frac{Prowess}{100})) $$
  • The last piece of information we need is the bleeding damage, which is dependent on condition damage (Malice). According to the GW2 wiki this is determined by $$ \frac{damage}{second} = 40+0.05 \cdot (Malice) $$. The bleed duration of 5 seconds can be improved through stats, but only pulses once per second. This means that we can round the duration down to find the number of pulses and find the total bleed damage: $$ \frac{damage}{second} \cdot \lfloor duration \rfloor $$

To get a rough estimate of Phantasm DPS, I put these formulas together with some various equipment set-ups and trait choices. You can download this spreadsheet here. To make things simplier, I focused entirely on “Illusionary Duelist” with SI because I knew it hits 8 times every 10 seconds. I also had to make several assumptions about how certain traits would stack, and all of this is subject to change when the game is released anyway. Despite these shortcomings, I found several interesting results:

  • Without any bonus condition damage, SI can add about 10%-20% damage depending on the target’s armor (best against higher armor foes) when used in conjunction with Phantasmal Fury. This puts it on par with most damage traits at the adept level.
  • With a skill coefficient of about 0.5 (a total guess BTW), the direct damage builds and condition damage builds I tried seem to even out in terms of potential damage. A lower skill coefficient tends to favor condition damage and a higher one favors direct damage.
  • Chaotic Transference bonus seems lack-luster relative to the heavy investment.
  • Phantasmal Strength and Empowered Illusions complement each other well in a power Build, but the investment for Phantasmal Strength doesn’t seem worth it in a condition damage build.
  • Phantasmal Haste tends to work better with a condition damage build than a power build. You don’t need to hit hard with SI, you just need to hit often.
  • Investing 20 points into Domination can have a big effect on condition damage builds because it extends bleeds for an extra tick. This makes Lyssa’s Runes a potentially interesting choice with SI because of the +10% condition duration, allowing you to spend 10 of those points from Domination elsewhere with minimal DPS loss.
  • The Rampager jewelry seems to be a better choice than Rabid for a condition damage build with SI. There’s no point to having strong bleeds if you aren’t applying them frequently enough.

There’s still a lot more analysis to be done here and some empirical data to collect in BWE3 to verify these findings, but the results look promising. As it stands, you can make SI work in either a direct damage phantasm build or condition damage build with the appropriate gear. Small tweaks to the skill coefficient can keep the two builds competitive if necessary. This fits with Arena.Net’s philosophy of having multiple play-styles be equally viable.

I’d encourage you to try out the spreadsheet with other gear and build combinations that I didn’t try. If you’re feeling adventurous, you might even extend it to include skills other than iDuelist or other traits I may have overlooked. If you find out any more information about how phantasm damage is calculated I’d love to hear about it in the comments!

Happy theory-crafting!

Update: BWE3

I did a little testing during BWE3, regarding the attack rates and skill coefficients of the different phantasms. This information should help give an idea of how much each phantasm benefits from stacking Power vs stacking crit/condition damage for Sharper Images. Please note that my recharge times were approximated, and Sanek over at GW2Guru came up with somewhat different numbers. I’m including both my attack rates and his for comparison:

illusion Hits Recharge Attack Rate (hits/sec) Sanek’s Recharge Sanek’s Rate (Hit/sec) Approx. Skill Coef. DPS Coef. (Mine) DPS Coef. (Sanek)
iDuelist 8 10 0.8 7.5 1.066666667 0.228956229 0.183164983 0.244219978
iSwordsman 1 3 0.333333333 5.5 0.181818182 0.734006734 0.244668911 0.13345577
iWarlock 1 5 0.2 6 0.166666667 0.080808081 0.016161616 0.013468013
iBerserker 1 5 0.2 6 0.166666667 0.281144781 0.056228956 0.046857464
iMage 1 5 0.2 6.7 0.149253731 0.397306397 0.079461279 0.059299462
iDefender 1 3 0.333333333 4.5 0.222222222 0.131313131 0.043771044 0.029180696
iDisenchanter 1 3 0.333333333 4.5 0.222222222 0.131313131 0.043771044 0.029180696
iWarden 12 10 1.2 14 0.857142857 0.033670034 0.04040404 0.028860029
swordClone 3 3 1
staffClone 1 1 1
scepterClone 2 3 0.666666667
gsClone 3 2 1.5

Knowing that the skill coefficient for iDuelist is only 0.23, stacking for condition damage seems to be the best method to maximize damage over time with Sharper Images given a high enough crit rate to apply it consistently. As a general rule of thumb, if your crit rate is less than 50% then you should be gearing for power and if your crit rate is greater than 50% then you should be gearing for condition damage.

A few other interesting things to note:

  • iSwordsman has one of the best skill coefficients of any phantasm. If you’re not using Sharper Images and have Power oriented spec, you may want to try out the off-hand sword.
  • iWarlock’s DPS is pretty pitiful without conditions. I’m not sure what the bonus per condition is, but I’d recommend having two staff clones up with iWarlock since they have a much faster attack rate. Edit: 10% bonus per condition
  • iWarden has quick attack rate and is has an AoE attack, but remember that this Phantasm is stationary. You’re very unlikely to get all 12 hits against a real player.
  • iBerserker has slow recharge AoE attack that moves down a line. It might be possible to hit an opponent twice with this if they’re running in the same direction, but I can’t be sure about it.
  • The Greatsword clones have the fastest attack rate of any illusion according to my tests. It seems kind of odd that the best clone for Sharper Images would be on a weapon with no innate condition damage.
  • iMage has a high skill coefficient but low attack rate. At first glance, this looks like it would be better for a power build than condition build, but you should remember that he also applies Confusion on attack.
  • iMage and iDisenchanter have bouncing attacks that hit three targets: 1 enemy and 2 allies. I couldn’t seem to get it to hit the same enemy twice, but this is something to check for on release.
  • Keep in mind that my original spreadsheet assumes that you leave your Phantasms out all the time. As of BWE3, this is no longer the optimal play-style. If you decide to go with a Power build, you’ll probably get the best burst damage by using Mind Wrack right after your phanstasm’s first attack cylce. Likewise, Cry of Frustration can now dish out some major hurt if you’re built for condition damage.

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In a previous blog post, I made the claim that much of the math curriculum is ordered based on historical precedent rather than conceptual dependencies. Some parts of the math curriculum we have in place is based on the order of discovery (not always, but mostly) and while other parts are taught out of pure habit: This is how I was taught, so this is how I’m going to teach. I don’t think this needs to be the case. In fact, I think that this is actually a detriment to students. If we want to produce a generation of mathematicians and scientists who are going to solve the difficult problems of today, then we need to address some of the recent advances in those fields to prepare them. Students should not have to “wait until college” to hear about “Topology” or “Quantum Mechanics”. We need to start developing the vocabulary for these subjects much earlier in the curriculum so that students are not intimidated by them in later years.

To this end, I’d like to propose 5 mathematical breakthroughs that are both relatively recent (compared to most of the K-12 curriculum) while also being accessible to elementary school students. Like any “Top 5”, this list is highly subjective and I’m sure other educators might have differing opinions on what topics are suitable for elementary school, but my goal here is just to stimulate discussion on “what we could be teaching” in place of the present day curriculum.

#1. Graph Theory (c. 1736)

The roots of Graph Theory go back to Leonard Euler’s Seven Bridges of Königsberg in 1736. The question was whether or not you could find a path that would take you over each of the bridges exactly once.

Bridges of Königsberg

Euler’s key observation here was that the exact shapes and path didn’t matter, but only how the different land masses were connected by the bridges. This problem could be simplified to a graph, where the land masses are the vertices and the bridges are the edges.

This a great example of the importance of abstraction in mathematics, and was the starting point for the field of Topology. The basic ideas and terminology of graph theory can be made easily accessible to younger students though construction sets like K’Nex or Tinkertoys. As students get older, these concepts can be connected to map coloring and students will be well on their way to some beautiful 20th century mathematics.

#2. Boolean Algebra (c. 1854)

The term “algebra” has developed a bad reputation in recent years. It is often referred to as a “gatekeeper” course, which determines which students go on to higher level mathematics courses and which ones do not. However, what we call “algebra” in middle/high school is actually just a subset of a much larger subject. “Algebra I” tends focuses on algebra as it appeared in al-Khwārizmī’s Compendious Book on Calculation by Completion and Balancing (circa 820AD). Consequently, algebra doesn’t show up in the math curriculum until students have learned how to add, subtract, multiply and divide. It doesn’t need to be this way.

In 1854, George Boole published An Investigation of the Laws of Thought, creating the branch of mathematics that bears his name. Rather than performing algebra on numbers, Boole used the values “TRUE” and “FALSE”, and the basic logical operators of “AND”, “OR”, and “NOT”. These concepts provided the foundation for circuit design and eventually lead to the development of computers. These ideas can even be demonstrated with a variety of construction toys.

The vocabulary of Boolean Algebra can and should be developed early in elementary school. Kindergartners should be able to understand basic logic operations in the context of statements like “grab a stuffed animal or a coloring book and crayons”. As students get older, they should practice representing these statements symbolically and eventually how to manipulate them according to a set of rules (axioms). If we develop the core ideas of algebra with Boolean values, than perhaps it won’t be as difficult when these ideas are extended to real numbers.

#3. Set Theory (c. 1874)

Set Theory has its origins in the work of Georg Cantor in the 1870s. In 1874, Cantor published a ground breaking work in which he proved that there is more than one type of infinity — the famous “diagonal proof“. At the heart of this proof was the idea of thinking of all real numbers as a set and trying to create a one-to-one correspondence with real numbers. This idea of mathematicians working with sets (as opposed to just “numbers”) developed momentum in the late 1800s and early 1900s. Through the work of a number of brilliant mathematicians and logicians (including Dedekind, Russell, Hilbert, Peano, Zermelo, and Fraenkel), Cantor’s Set Theory was refined and expanded into what we know call ZFC or Zermelo-Fraenkel Set Theory with the Axiom of Choice. ZFC was a critical development because it formalized mathematics into an axiomatic system. This has some suprising consequences such as Gödel’s Incompleteness Theorem.

Elementary students probably don’t need to adhere to the level of rigor that ZFC was striving for, but what is important is that they learn the language associated with it. This includes words and phrases like “union” (“or”), “intersection” (“and”), “for every”, “there exists”, “is a member of”, “complement” (“not”), and “cardinality” (“size” or “number”), which can be introduced informally at first then gradually formalized over the years. This should be a cooperative effort between Math and English teachers, developing student ability to understand logical statements about sets such as “All basset hounds are dogs. All dogs are mammals. Therefore, all basset hounds are mammals.” Relationships can be demonstrated using visual aids such as Venn diagrams. Games such as Set! can further reinforce these concepts.

#4. Computation Theory (c. 1936)

Computation Theory developed from the work of Alan Turing in the mid 1930s. The invention of what we now call the Turing Machine, was another key step in the development of the computer. Around the same time, Alzono Church was developing a system of function definitions called lambda calculus while Stephen Kleene and J.B Rosser developed a similar formal system of functions based on recursion. These efforts culminated in the Church-Turing Thesis which states that “everything algorithmically computable is computable by a Turing machine.” Computation Theory concerns itself with the study of what we can and cannot compute with an algorithm.

This idea of an algorithm, a series of steps to accomplish some task, can easily be adapted for elementary school instruction. Seymour Papert has been leading this field with technologies like LOGO, which aims to make computer programming accessible to children. Another creative way of approaching this is the daddy-bot. These algorithms don’t need be done in any specific programming language. There’s much to be learned from describing procedures in plain English. The important part is learning the core concepts of how computers work. In a society pervaded by computers, you can either choose to program or be programmed.

#5. Chaos Theory (c. 1977)

Last, but not least, is Chaos Theory — a field of mathematics that developed independently in several disciplines over the 1900s. The phrase “Chaos Theory” didn’t appear in the late 1970s, but a variety of phenomena displaying chaotic behavior were observed as early as the 1880s. The idea behind Chaos Theory is that certain dynamic systems are highly sensitive to initial conditions. Drop a shot of half-half into a cup of coffee and the resulting pattern is different every time. The mathematical definition is a little more technical than that, but the core idea is relatively accessible. Chaos has even found several notable references in pop culture.

The other core idea behind chaos theory is topological mixing. This could be easily demonstrated with some Play-Doh (or putty) of two or more colors. Start by combining them into a ball. Squash it flat then fold it over. Repeat it several times and observe the results.

The importance of Chaos Theory is that it demonstrates that even a completely deterministic procedure can produce results that appear random due to slight variations in the starting conditions. This can even be taken one step further by looking at procedures that generate seeming random behavior independently of the starting conditions. We live in an age where people need to work with massive amounts of data. The idea that a simple set of rules can produce extremely complex results provides us with tools for succinctly describing that data.

Conclusion

One of the trends in this list is that these results are easy to understand conceptually but difficult to prove formally. Modern mathematicians seem to have a tendency towards formalism, which is something of a “mixed blessing”. On one hand, it has provided mathematics with a firm standard of rigor that has withstood the test of time. On the other hand, the language makes some relatively simple concepts difficult to communicate to younger students. I think part of the reason for this is that the present curriculum doesn’t emphasize the rules of logic and set theory that provide the foundation for modern mathematics. In the past, mathematics was driven more by intuitionism, but the math curriculum doesn’t seem provide adequate opportunities for students to develop this either! It might be argued things like “new math” or “Singapore math” are helping to develop intuitionism, but we’re still not preparing students for the mathematical formalism that they’ll be forced to deal with in “Algebra I” and beyond. Logic and set theory seem like a natural way to develop this familiarity with axiomatic systems.

Observers might also note that all five of these proposed topics are related in some form or another to computer science. Computers have been a real game-changer in the field of mathematics. Proofs that were computationally impossible 500 years ago can be derived a in minutes with the assistance of computers. It’s also changed the role of humans in mathematics, from being the computer to solving problems using computers. We need to be preparing students for the jobs computers can’t do, and my hope is that modernizing the mathematics curriculum can help accomplish this.

Do you have anything to add to this list? Have you tried any of these topics with elementary students? I’d love to hear about your experiences in the comments below.

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Gary Davis (@republicofmath) wrote an article that caught my attention called What’s up with pre-calculus?. In it, he presents a number of different perspectives on why Pre-Calc classes have low success rates and do not adequately prepare students for Calculus.

My perspective on pre-calculus is probably far from the typical student, but often times the study of “fringe cases” like myself can provide useful information on a problem. The reason why my experience with Pre-Calc was so atypical, is because I didn’t take it. After taking Algebra I, I had started down a path towards game programming. By the end of the following year, where I had taken Geometry, this little hobby of mine hit a road block. I had come to the realization that in order to implement the kind of physics that I wanted in my game I would need to take Calculus. I petitioned my counselor to let me skip Algebra II and Pre-Calc to go straight into AP Calculus. They were skeptical at first, but eventually conceded to my determination and allowed me to follow the path I had chosen.

Skipping from Geometry to Calculus meant that there were a lot of things that I needed to learn that first month that many of my peers had already covered. I had never even heard the word “logarithm” before, had no idea what e was, and had only a cursory understanding of trigonometry. These were the topics I had missed by skipping Pre-Calc, and I was fully aware of that, so I “hit the books” and learned what I needed to know about them. By the end of that first month I had caught up to the rest of the class and by end of the semester I would be helping other students with those very same topics.

I think the most obvious difference between myself and the “typical Calculus student” was the level of motivation. Many of the students in Calculus were there because “it would look good on a college application”. I was there because I wanted to be there. A common problem throughout math education is the “When am I ever going to use this?” attitude. I already knew where I was going to use the math I was learning. I had an unfinished game at home that needed a physics system, and every new piece of information I learned in Calculus made me one step closer to that goal. If you had ever wondered why a 4th order Runge-Kutta method is better than Euler’s method, try writing a platformer.

The second difference was a little more subtle, but there were some conceptual differences in how I thought about exponential, logarithmic, and trigonometric functions. The constant “e” wasn’t just some magic number that the textbook pulled out of thin air, it was the the unique number with the property that $$ \frac{de^x}{dx} = e^x $$ and $$ \int e^x dx = e^x $$. When it came to sine and cosine, I would think of them like a circle while my other classmates would picture a right triangle. They would hear the word “tangent” and think “opposite over adjacent”, but I thought of it more like a derivative. Sure, I had to learn the same “pre-calc” material as they did, but the context of this material was radically different.

A couple years ago I suggested that Pre-Calc should be abolished. The trouble with Pre-Calculus (at least in the U.S.) is that the course needs to cover a very diverse array of questions which includes exponential, logarithmic and trigonometric functions. I would argue that these concepts are not essential to understanding the basic foundations of Calculus. The math curriculum introduces the concept of “slope” in Algebra I, which is essentially the “derivative” of a line. There’s no reason why we should be sheltering students from language of Calculus. The concepts of “rate of change” and “accumulation” can and should be connected with the words “derivative” and “integral”, long before students set foot in the course we presently call Calculus. As students become more comfortable with these concepts as they relate to lines, parabolas and polynomials, then gradually step up the level of complexity. When students start to encounter things like surfaces of revolution, then they’ll actually have a reason to learn trigonometry. Instead of trigonometry being the arbitrary set of identities and equations that it might appear to be in pre-calc, students might actually learn to appreciate it as a set of tools for solving problems.

I think this issue of Pre-Calc is really a symptom of a larger problem. The mathematics curriculum seems to be ordered historically rather than conceptually. I’ve heard Pre-Calc described as a bridge to Calculus. This makes sense when you consider the historical development of Calculus, but not when considering the best interest of students in today’s society. Leibniz and Newton didn’t have computers. Who needs bridges when you can fly?

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At long last, I finally got my chance to play Guild Wars 2! An ambitious title to say the least, GW2 is leaps and bounds ahead of its predecessor. I clocked in as much time as I could over the beta weekend, and am now going through withdrawal so I thought I’d take this opportunity to share my experiences. I had hoped to record some video over the weekend, but the performance impact was a little more than I expected. A choppy YouTube video would hardly do this game justice, so you’ll just have to settle for a written account.

As a mesmer primary in the original Guild Wars, it should be no surprise that I gravitated towards this class in GW2. I had my concerns about how this class would carry over, but any doubts that I had are now gone. The GW2 mesmer uses completely different game mechanics than the GW1 Mesmer, but it still captures the essential feeling of the class. I played the mesmer class through the end of the BWE personal story line at level 18, and spend the rest of my time playing PvP with various classes.

Coming from GW1, I had a lot of preconceived notions as to what GW2 would be like. It makes sense to organize these into the parts I overestimated and parts I underestimated. These are not necessarily pros and cons, but simply differences between how I thought GW2 would work and how it actually worked. Keep in mind that the game is still a work in progress, and I’m trying to give an honest opinion so that it can be made even better in the future.

Since I spent the most time playing a mesmer, that’s probably the best place for me to start. From the very beginning of the game, it became clear that I had overestimated the shatter skills and underestimated the phantasm skills. Don’t get me wrong, a Mind Wrack with both traits is definitely a force to be reckoned with, but it’s just that I thought that the Mind Wrack traits and a high level of Guile would be essential to any mesmer build. It turned out that this wasn’t the case and there were other viable ways of playing the class. In fact, the phantasms were so awesome that I was usually hesitant to shred them. The three illusion limit also meant that I had to be careful about when I used my clones to not overwrite my phantasms. Since the illusions are locked on to a single target, this added an additional incentive to shred them before the target dies. All of these considerations made the shatter skills something that required careful timing and not just another skill to spam.

As far as the mesmer weapons are concerned, I think I overestimated the scepter and underestimated the staff. The scepter was great at pumping out clones, but I ended up relying on phantasms for most of my damage and it was hard to keep up confusion in PvP. On the other hand, I found myself enjoying the staff a lot more than I expected. The idea of random conditions and boons was something of a turn off for me when I first read the skill descriptions, but the way that it worked was that offensive buffs/debuffs were tied to offensive skills and the defensive buffs/debuffs were tied to defensive skills. Even though the results were random, they were still something that was useful in the situation.

Slightly related to the points above, I think I overestimated the confusion condition and underestimated poison. I think that part of this was that I was trying to compare confusion with hexes like Empathy and Backfire in GW1, where a whole stack of hexes becomes problematic to remove. A whole stack of confusion in GW2 still only counts as one condition, making it relatively easy to remove — if it was even worth removing at all. On the other hand, I somehow missed the memo about poison reducing healing by 33%. This healing reduction coupled with a sometimes deceptively long duration made poison into one of the more threatening conditions for me. I distinctly remember this one thief that I fought where I had to keep spamming my healing skill until my condition removal was up again to avoid dying from poison long after I had killed him. By the time I was able to remove it, he had respawned and was back for more while I was still at 25% health — ouch.

One of the other things that caught me off guard was that I overestimated Vitality and underestimated Toughness. In GW1, gearing for PvP was quite simple: stack as much health as you can. GW1 had a large number of armor ignoring damage sources and having enough health to survive a large damage spike was essential to surviving long enough for the healers to react. In GW2, there are no “healers”. I found that rather than dealing with a single large damage spike, sustained damage was much more of a threat. This made it more practical for me to focus on improving damage mitigation rather than just stacking health. Of course, this might also be a function of beta players not using voice chat to coordinate spikes.

In terms of the PvP modes, I think I overestimated “Structured PvP” and underestimated “World vs World”. I spent a lot of time playing Random Arenas in GW1 and it seemed like the “Structured PvP” was going to be right up my alley. I enjoyed the Structured PvP in GW2, but I think that was mainly because it gave me a chance to play with a fully leveled and unlocked character. The problem I had with Structured PvP it was that it felt too much like an FPS match to me. Win or lose, you were queued for the next match on the same server, fighting the same opponents with the same team over and over until someone leaves. Despite the best efforts of the game to auto-balance the teams, they were often off by one player which makes a big difference with smaller numbers. Nothing like fighting a 2 on 1 battle to ruin the fun. I also spotted a couple of “leechers” in the beta, which I thought was kind of odd. Its not like it was worth farming Glory in the beta, so I’m assuming that they just went AFK and forgot about it. However, “World vs. World” was a completely epic experience. Despite the fact that none of us really knew what we were doing, the sheer number of people on the battlefield was a sight to behold. In comparison to World of Warcraft, World vs World seemed like Alterac Valley on steroids with added benefits outside of the battleground. The only downside to World vs World that I saw was that the repair costs could rack up quickly if you were careless.

All in all, I think Guild Wars 2 met and then exceeded my expectations in a lot of areas. If I were to make a comparison, it felt like Guild Wars 2 was like the MMO equivalent of an Elder Scrolls game. The starting “tutorial zones” seemed less like a tutorial and more like a story “hook” — my favorite of which being the Charr. The dynamic event system made questing feel less like a grind and more like a sandbox. There’s a main story if you want to follow it, or you can just go explore the world and do whatever you like.

I also felt like I had a great amount of freedom in how to play my class. The build I finally settled on with my mesmer in PvP was this one. The Illusionary Warlock and Illusionary Duelist combination packed some serious damage while the Chaos traits and crippling clones made me pretty difficult to kill. Chaos Storm and Null Field allowed me to skill combo by myself for extra conditions. The Portal skill was simply amazing in Conquest mode for feigning retreat from a node, only to return later with reinforcements. The only downside of this build was that I had to be careful when swapping the scepter so that I didn’t overwrite my phantasms with clones — I would just use the two pistol skills and the channeled confusion skill then immediately swap back to the staff. In PvE I replaced the pistol with a focus and Portal with Blink to get around faster, since the burst damage wasn’t as important.

Another hidden surprise was the crafting system. I didn’t get much time to play with it, but it seemed to be a nice balance between the “discovery” system of Final Fantasy XI and the “recipe list” system of World of Warcraft. You combine random materials to learn new recipes, but once you learn they are added to the recipe list. As an added bonus, it seemed to accelerate the crafting process when I was creating items in bulk! It’s the little details like that which made me feel GW2 was respecting the time I spent playing.

Are you a long time Guild Wars player that participated in the GW2 Beta? What did you underestimate or overestimate about the sequel?

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Is “rationality” a measurable quantity?

In a previous blog post, I discussed some common logical errors that often arise in political discourse. This led to a rather interesting discussion on Twitter about political behaviors and how to model them mathematically (special thanks to @mathguide and @nesa_k!). One of the questions that came up this this discussion was how to define “rational behavior” and whether or not this is a measurable quantity. What follows is my hypothesis on “rational behavior”: what it is and how to measure it.

Please keep in mind that this is just a hypothesis and I don’t quite have the resources to verify these claims experimentally. If anyone has evidence to support or dispute these claims, I would certainly be interested in hearing it!

Defining “rational behavior”

Before we can begin to measure “rationality”, we must first define what it means to be “rational”. Merriam-Webster defines “rational” as “relating to, based on, or agreeable to reason”. The Online Etymology Dictionary describes the roots of the word in the Latin rationalis, meaning “of or belonging to reason, reasonable”, and ratio, meaning “reckoning, calculation, reason”. It’s also worthwhile to mention that ratio and rational have a distinct mathematical definition referring to the quotient of two quantities. Wikipedia suggests that this usage was based on Latin translations of λόγος (logos) in Euclid’s Elements. This same Greek word lies at the root of “logic” in English.

Based on these definitions and etymology, I think its fair to define rational behavior as “behavior based on a process of logical reasoning rather than instinct or emotion”.

Even this definition is far from perfect. In the context of game theory, “rational behavior” often defined as the process of maximizing benefits while minimizing costs. Note that by this definition, even single celled organisms like amoeba would be considered to exhibit “rational behavior”. In my opinion, this minimax-ing is a by-product of evolution by natural selection rather than evidence of “reason” as implied by the typical usage of the word “rational”.

I should also clarify what I mean by “logical reasoning” in this definition. In trying to quantitatively measure rational behavior, I propose that it makes sense to use a system of fuzzy logic rather than Boolean logic. By using the Zadeh operators of “NOT”, “AND”, and “OR”, we can develop an quantitative measure of rationality on a scale of 0 to 1. In logic, we say that an arguement is considered sound if it’s valid and its premises are true. Since we’re using the fuzzy “AND” in this model, the rationality measure is the minimum truth value of the logical validity and base assumptions.

Using this definition, we can also define irrational behavior as “behavior based on an invalid logical argument or false premises”. I’d like to draw a distinction here by defining arational behavior as “instinctive behaviors without rational justification”, to cover the amoeba case described above. An amoeba doesn’t use logic to justify its actions, it just instinctively responds to the stimuli around it.

Rationalism and Language

There’s an implicit assumption in the definition of “rational behavior” that I’ve used here, and that is that this requires some capacity for language. First-order predicate logic is a language, so the idea that “rational behavior” is language dependent should come as no surprise. In fact, the same Greek word “logos” from which “rational” is derived was also used as a synonym for “word” or “speech”. The components of language are necessary for constructing a formal system, by providing a set of symbols and rules of grammar for constructing statements. Add a set of axioms (assumptions) and some rules for inference, and you’ll have all the components necessary to construct a logical system.

A Dynamic Axiomatic System Model of Rational Behavior

A this point we can start to develop an axiomatic system to describe rational behavior. Using the operators of fuzzy logic and the normal rules of first-order logic we can create an axiomatic system that loosely has the properties we would expect of “rational behavior”. It’s very unlikely that the human mind uses the exact rules of fuzzy logic, but it should be “close enough”. We also have to consider that the basic beliefs or assumptions of a typical person vary over time. Thus, it’s not enough to model rational behavior as an axiomatic system alone, we must consider how that system changes over time. In other words, this is a dynamic system.

As we go through life, we “try out” different sets of beliefs and construct hypotheses about how the world works. These form the “axioms” of our “axiomatic system”. Depending on whether or not these assumptions are consistent with our experiences, we may decide to keep those axioms or reject them. When this set of assumptions contains contradictions, the result is a feeling of discomfort called cognitive dissonance. This discomfort encourages the brain to reject one of the conflicting assumptions to reach a stable equilibrium again. The dynamic system resulting from this process is what I would characterize as rational behavior.

One particularly powerful type of axiom in this system is labeling. Once a person takes a word or label and uses it to describe him or herself, the result is the attribution of large number of personal characteristics at once. The more labels a person ascribes to, the more likely it is that a contradiction will result. Labeling also has powerful social effects associated with it as well. Ingroups and outgroups can carry with them substantial rewards or risks depending on the context.

Rather than rejecting faulty axioms when confronted with cognitive dissonance, some individuals develop alternative methods of reducing the discomfort. The general term for pattern of behavior is called cognitive bias. This behavior can take a variety of different forms, but the one that is most relevant to this discussion is the confirmation bias. One of the ways in which the human brain can reduce the effects of cognitive dissonance is by filtering out information that would result in a contradiction with the base assumptions. Another relevant bias to consider is the belief bias, or the tendency to evaluate the logical validity of an argument based on a pre-existing belief about the conclusion.

Whatever form it may take, cognitive bias should be taken as evidence of “irrational behavior”. Not all cognitive biases are of equal magnitude, and some arguments may rely more highly on these biases than others. The goal here is not a Boolean “true” or “false” categorization of “rational” and “irrational”, but more of a scale like the one used by PolitiFact: True, Mostly True, Half-True, Mostly False, False, Pants on Fire. The method of applying truth values in fuzzy logic makes it highly appropriate for this purpose.

Examples in Politics

Consider this clip from The Daily Show. Using this clip may seem a little biased, but it’s important to remember that John Stewart is a comedian. Comedians have an uncanny knack for walking the fine line between “rational” and “irrational”, providing an interesting perspective to work with.

In the first example, we have the issue of Rick Santorum and JFK. After reading JFK’s speech on religious freedom, Santorum says that it made him want to throw up. In order to defend this statement, Santorum uses a good ole fashioned straw man argument by claiming that JFK was saying “no faith is not allowed in the public public square” when in fact JFK was saying “all faiths are allowed”. I think Santorum’s behavior here is a prime example of irrational behavior. Taking this position may very well earn him some votes with the deeply religious, but it’s clear that Santorum has some problems finding consistency between his personal beliefs and the First Amendment. His position is not based on a valid logical argument, but on a physical response to the cognitive dissonance resulting from his conflicting beliefs. This example also shows the power of deeply held self-labeling behaviors like religion.

Mitt Romney made some headlines with his “NASCAR Team Owner” blunder. It would appear that Mitt Romney had gone to Daytona to try and score some points with “average Americans”, but a slip of the tongue showed how out of touch he really is. To Romney’s credit, his behavior here is about half-rational. His assumptions are probably something like this:

  • I want people to vote for me.
  • People vote for someone they can relate to.
  • Most people know someone who likes NASCAR.
  • I know someone who likes NASCAR.

It makes sense from a logical standpoint, but it turns out that the person who Romney knows that likes NASCAR just happens to be a
“team owner” instead of a “fan”. This small detail makes it unlikely that people will relate to him, but at least the foundation of a logical argument is there.

This brings us back to Rick Santorum again. This time, Santorum calls President Obama a “snob” for “[wanting] every American to go to college”. Not only is this comment blatantly false, but he’s employing an ad hominem attack in lieu of a logical argument. This example draws a nice dichotomy between President Obama and Rick Santorum. The President is making a rational argument in favor of higher education which is well supported by evidence. By opposing this rational argument on a faulty premise, Santorum comes out of this situation looking mostly irrational. His behavior makes sense if you consider the effects of confirmation bias. Santorum believes that the President is trying to indoctrinate college students to become liberals. He believes it so thoroughly that he simply filters out any evidence that would contradict it. While most observers can hear the President say “one year of higher education or career training“, Santorum doesn’t. He hears the part confirms his beliefs and filters out the rest. I’d imagine that for Santorum, listening to President Obama speak sounds something like the teacher from the Peanuts cartoons: “one year of higher education wah wah-wah wah-wah-wah“. To Santorum’s credit, at least he had the mind to retract his “snob” statement — even if only partially. This shows that the underlying mechanisms for rational behavior are still there, despite his frequent leaps of logic.

Conclusion

I hope I’ve at least managed to present a definition of “rationality” that’s a little more precise than the everyday use of the term. I’m sure some people out there might disagree with the way I’ve rated the “rationality” of these behaviors. Different people have different experiences and consequently have different assumptions about the world. If we were to use multiple “rationality raters” and average the results, perhaps we might have a decent quantitative measure of rationality to work with.

Part of the problem with measuring rationality is the speculative nature of trying to determine someone else’s assumptions. We can generally use what a person says as an indication of what they believe — at least for the most part. It’s also important to consider not only the statement, but the context in which the statement is made. In political discourse, we implicitly assume that politicians are being honest with us. They might be wrong about the facts, but this idea that they are honestly representing their own views is something that voters tend to select for. Perhaps this is why Romney is still struggling against Santorum in the primary. Santorum may have problems getting his facts straight and presenting a logical argument, but he has a habit of saying what he believes regardless of the consequences. Romney, on the other hand, says what he thinks will win him the most votes. Many voters do not vote “rationally”, they vote according to how they “feel” about the candidates. Romney may be more “rational” than Santorum, but his calculated responses cause him to lose that “feeling of honesty” that Santorum elicits from voters.

In the next article, I’ll attempt to explain the origins of rational and irrational behavior. I think the key to understanding these behaviors lies in evolution by natural selection. I would argue that both rational and irrational behaviors contributed to the survival of our species, and this is why irrationality persists into the present. Stay tuned!