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29 December 2009

Riding Out the Swarm

The Heroic Anub'arak encounter places great strain on a 10-man raid attempting it. Teams with a relatively weak dps team may choose to bring two healers into it, placing a great burden on the healing team during Phase 3.

Phase 3 is notorious for Leeching Swarm that Anub'arak keeps up during this time. This is coupled with a heavily ticking Penetrating Cold debuff cast on three random players. Due to high-hitting melee attacks and Freezing Slash, one healer usually must focus 100% on healing the main tank, leaving the other healer handling the raid and the offtank. That raid healer has a hard job, though a few tips and tricks may make it much easier.

26 December 2009

WoW Mathematics: Fatally Attracted to You

Back in the Burning Crusade era, Mother Shahraz was notorious for the encounter's high Shadow Resistance requirement and her femininity. She would also, at random times, cast Fatal Attraction on three random non-tank players.

Despite having Shadow Resistance at the cap, the damage is still great, and the unlucky trio need to separate promptly if they are to survive. It may be useful to know, given a certain set of vectors and using calculus, how fast they are moving away from each other...

18 December 2009

Father rescues son from Icecrown Citadel

The Deathbringer Saurfang encounter provides for a very tantalising and moving lore moment. Not only is the more recent death knight dilemma explored, but also it draws from history as far back as the First War.

A father (Varok Saurfang, also known as High Overlord Saurfang ingame) talks to the reanimation of his son (Dranosh Saurfang, the Younger), the latter of which is obstructing the former's passage. A commentary on the more detailed Horde version of the dialogue is offered in a Q&A format.

High Overlord Saurfang yells: Kor'kron, move out! Champions, watch your backs! The Scourge have been...
Deathbringer Saurfang yells: Join me, father. Join me and we will crush this world in the name of the Scourge. For the glory of the Lich King!

14 December 2009

Names of Raid Target Icons

Each of the eight raid target icons (also raid icons or lucky charms) are referred to with common (and usually standard) names. However, for some of them, the names used in mathematics are different.

A few definitions
  • Shape: An object occupying space, distinguished by its perimeter (outer boundary).
  • Plane figure: A shape occupying a two-dimensional plane.
  • Quadrilateral: A plane figure with four straight sides
  • Parallelogram: A quadrilateral with opposite sides parallel to each other respectively.
  • Rectangle: A parallelogram with at least one vertex (corner) a right angle.

30 November 2009

RuneScape's Cryptic Clue Fest: A Retrospect

On 26 November 2009, following a system update, Mod Howes (pictured to the right) started the Cryptic Clue Fest, a series of puzzles sending players throughout the F2P world. All puzzles were needed to be done in sequence to finish the whole exercise.

Each step required talking to certain NPCs while carrying the correct quantities of various 'code items'. To find out which, how many and who, various cryptic messages needed to be deciphered: some involving interpretation and some involving mathematics. The Clue Fest proved to be very challenging to players with a poor wield of various skills and knowledge.

27 November 2009

My Computer and I: Rat-a-tat-a-tat

My desktop is a 3-year-old Dell Dimension 8400. It was high-end at the time it was bought, but regardless is starting to show its age. I have upgraded some of its parts since then to keep playing World of Warcraft bearable, but of course it will need to be replaced eventually.

I have had my share of computer problems with my current computer (not suggesting that Dell is necessarily a poor computer assembler, mind you). Other than high school computing studies, I have had no formal training in maintaining a computer, so I usually need to end up experimenting when something goes wrong. Without further ado...

The Problem:
I had upgraded the video card (to an NVIDIA GeForce 8400 GS). After its installation, the computer tower would emit a noticeable low-pitch rattling sound. It was easily recognised as percussion and distinct from beeps emitted from the system speaker.

17 November 2009

Random Ramblings to 17 November 2009

Acidosis
An increase in the acidity (or a decrease in the pH) of blood. The eventual state of highly acidic blood is referred to as acidaemia. The pH of blood must be kept near 7.4 (slightly basic) or the body will not be able to function properly. One type of acidosis occurs when carbon dioxide (CO2) is not released through the lungs fast enough, causing a buildup of carbonic acid (H2CO3). Another type of acidosis (lactic acidosis) occurs from excessive anaerobic respiration, where instead of using oxygen to break down sugar to release energy, the body instead breaks the sugar down into lactic acid. The lactic acid itself does not cause the acidity, but rather the respiration process. This commonly happens when sleeping on an arm, which becomes numb and experiences a pins-and-needles sensation when blood circulation is finally restored.

08 November 2009

A simple gear score

There exists several ways to rate the items a player has equipped (examples include gear scores from Be Imba, Armory Light and the GearScore addon. Each method places varying importances on different characteristics of the gear. While changes in single gear scores can track the player's gear progression, different gear scores cannot be compared with each other, or to any other benchmark.

There is another, simpler way to rate the quality of gear. Every item has an item level (ilvl), which Blizzard calculates from from the statistics (stats) they assign to it. Generally, the more stats there are on the item, the higher the ilvl. Why not base a gear score on a stat sanctioned by Blizzard?

30 October 2009

WoW Mathematics: Programming Your Warlock Tank

In a few rare NPC encounters, a warlock may be needed to tank a boss. Examples include Mimiron's Aerial Command Unit and Leotheras the Blind in Demon Form. While the focus of the warlock is to maximise threat, they may be interested in maximising DPS while generating the minimum amount of threat needed to hold aggro.

Fortunately, they have the mathematical tool of programming (not to be confused with programming computers) to work with. In its simplest form, linear programming, a certain value (e.g. profit, costs, or in this case a warlock tank's DPS) will need to be optimised (maximised or minimised). Of course, two chosen factors will influence that value (for this case, the number of casts of Shadow Bolt and Searing Pain), and, subject to several constraints, the right combination of both will need to be found.

This exercise gives a little insight to the workings of stat optimising utilities like Rawr.

24 October 2009

The Time-Value of Health

This blog post builds on the concepts suggested in 'Not All Hitpoints are Created Equal', helping to adjust healing for the health level of the recipient.

Experts in finance speak of the time-value of money. Under this concept, the value of a certain quantity of dollars (or other currency) will decrease as time passes. Many attribute this to the fact that people want money now rather than later. Therefore, to keep this time-value the same, interest must be paid on top of this quantity of dollars.

Hitpoints restored by healing also seem to have this time-value, since a heal of the same size will be more valued the sooner it is received (considering that people wish to keep their health at a maximum). How should such heal weighting be done?

16 October 2009

Of Ladders, Mirrors and Black Cats

Superstitious people may believe that performing certain actions endow bad luck on the one performing them, causing them great misfortune in the future. Are these worries justified?

Inspecting these superstitions further, it becomes evident that they do have substance, even if only a little! Think twice before doing any of the following...


Why should you not step on a crack on a footpath?
  • If not careful, you could get your foot caught in one and trip.

30 September 2009

Five reasons to like (Northrend) Ghouls

World of Warcraft's portrayals of things are noticeably cartoony when compared to real life equivalents. Northrend ghouls (ghouls) are no different, being any combination of cute, adorable, cuddly, pitiable, likeable and silly.

1. Descent into undeath
These lumbering, rotting corpses were once innocent townsfolk who have made the final transition into true undeath... They are vicious creatures, retaining little of their humanity. The plague has torn away most of their memories, leaving only hunger and basic survival instincts in their place... Even those who were close to the individual in life have difficulty recognizing their loved one; the transformation removes most vestiges of humanity as well as identifying features of voice and body structure.
WoWWiki

19 September 2009

Responsible Guild Leadership

Government is a human institution that exists to exact order on an otherwise chaotic society. Its citizens willingly surrender some amount of freedom to be able to take some solace in a sense of security.

Because government is conceived by the people, it must uphold the interests of the people, lest its purpose be defeated. Responsible government is a principle that attempts to achieve this by giving the people a direct say, or at least allow them to elect representatives. Under this framework, the government becomes directly responsible or accountable to the citizens it governs.

This widely accepted (by many democratic countries) principle can readily be applied to guild leadership in
World of Warcraft. The guild's officers simply need to act in the best interests of the membership.

11 September 2009

Succeeding at not being trampled

FailBot has been retired, but EnsidiaFails has taken over! What remains the same is the humiliation that arises if a boss ability, if avoidable, is not handled properly.

In the Trial of the Crusader, the Northrend Beast Icehowl casts Massive Crash, which can send players scattered throughout the instance. If players do not move out in time to avoid the following Trample, the situation can become very messy (in both senses of the word!).

09 September 2009

Dilemmas in Guild Matchmaking and Promotion

In the ideal world, prospective guild members would quickly find the guild of their dreams, and the guild would swiftly recruit them. However, in reality, asymmetric information exists, and this hampers the guild matchmaking process.

Asymmetric information occurs when one party (in this case, the person or guild) knows something that the other does not, and such knowledge cannot easily transfer from one to the other. This may be because of significant distance between the two, or one does not quite believe what the other claims.

04 September 2009

WoW Mathematics: My Large Brown Sack

To help find items easily, players often organise them in their bags in a certain way. It might be interesting to know just how many ways those items can be arranged, and what happens of those arrangements are restricted in some way.

Permutations are very useful in this process. It is a special case of the fundamental counting technique where an object, once picked, cannot be picked again, and so the available pool of objects decreases by one each time. Consider a certain 10-slot bag, the Large Brown Sack...

26 August 2009

Making Sense of Financial Statement Ratios

Many basic features of a business' business can be gleaned from their set of financial statements. However, the more intricate details can be found through ratio analysis.

The financial statement's figures are measured in currency units, which have little value in themselves because they do not consider the scale of business operations. By comparing relative sizes of these figures, this problem with units of measurement are eliminated by removing the units entirely. The resulting ratios are scale-free and can be used in comparing:
  • Two businesses of different sizes
  • The same business as it grows (or collapses) over time.

Analysts have devised myriad ratios to use in this type of analysis. What do they mean in real-world terms?

21 August 2009

Five reasons to like Bears

World of Warcraft's portrayals of things are noticeably cartoony when compared to real life equivalents. Bears and druids in Bear Form are no different, being any combination of cute, adorable, cuddly, pitiable and likeable.

This regular will dissect the art of various characters to identify some features that appeal to the inner child.

1. Wide abdomen
A wide figure appeals to the touch when hugging, especially if it is soft and plushy. There is little question to why bear hugs, in particular, feel so nice!

15 August 2009

Ulduar Protocol


I have seen worlds bathed in the Makers' flames. Their denizens fading without so much as a whimper. Entire planetary systems born and raised in the time that it takes your mortal hearts to beat once... A million, million lives wasted. Had they all held within them your tenacity? Had they all loved life as you do?
Algalon's dying breath

Considering the tremendous amount of history contained in the Storm Peaks, it might be worth finding out how Ulduar got there. A history of Azeroth's defense mechanisms follows. It all started during the Ordering...

Parasitic, necrophotic symbiotes
Azeroth was not as peaceful and beautifully formed as it currently is. Before the Titans' arrival, the elements would rage across the world in endless conflict, and the Old Gods would exact chaos upon it.

08 August 2009

Random Ramblings to 8 August 2009

Archivist
A person who maintains the material in an archive. This can involve collecting, organising and assessing the records. Among their skills, they show expertise in preserving the physical media on which information is contained. In WoW, Auriaya is the archivist for the secrets of Ulduar.

Information asymmetry
A concept in economics which suggests that buyers and sellers in a real-world market cannot find each other easily (lacking information about each others' presence). One needs to search for the other before a trade can occur. However, doing extra searching will come at a cost, so these costs should be balanced against the benefits expected in deciding which to do.

02 August 2009

Archavon's Parade


Which better way to Wintergrasp's Titan Relic than a beeline? The Scourge successfully employed this strategy in invading the Sunwell, after all (though their sheer numbers may have had something to do with it). This 160-man raid may now be trying to squeeze through an instance portal to Archavon...


It would be interesting to note Blizzard's use of perspective in this shot (where parallel lines seem to meet at a certain vanishing point). The above annotated image is provided for convenience.

29 July 2009

There's Something About Lady RNG

Computerised environments intrinsically lack randomness, so a random number generator (RNG) must be used where an unpredictable result is required. In effect, the RNG works on randomly generated data provided to generate a seemingly random number. Since this piece of programming code decides your fate and destiny in WoW in several cases (just like how Fortuna (Lady Luck) decides your fate and destiny in real life), it helps to know a bit about probability!

The golden rule of probability
Probability
is that branch of mathematics that deals with random phenomena to (among other things) determine how likely it will act in a certain way. It is important to know that, for truly random phenomena:
Random does not necessarily mean even or fair!

26 July 2009

My Computer and I: Connection Degeneration

My desktop is a 3-year-old Dell Dimension 8400. It was high-end at the time it was bought, but regardless is starting to show its age. I have upgraded some of its parts since then to keep playing World of Warcraft bearable, but of course it will need to be replaced eventually.

I have had my share of computer problems with my current computer (not suggesting that Dell is necessarily a poor computer assembler, mind you). Other than high school computing studies, I have had no formal training in maintaining a computer, so I usually need to end up experimenting when something goes wrong. Without further ado...

The Problem:
World of Warcraft's latency would be satisfactory when first logging on, but would increase over time, eventually causing WoW to disconnect.

21 July 2009

Not All Hitpoints are Created Equal

There is always question on whether the output of healing meters (healing charts) can be used in indicating a healer's performance. Unlike points of damage, where heals go matters. While everyone has use for a heal, some players will need it more than others.
 Healing meters (such as the 'Healing done' component of Recount) collect raw figures from the combat log. It becomes easy to assert, from skimming over the healing chart, that all hitpoints (HP) are created equal, with all players appreciating 1 HP of healing equally. However, I would not.

1. Factoring in absorptions
When a player inevitably takes damage, a healer can respond to it in any of two ways:

16 July 2009

WoW Mathematics: Your guild bank donation

Aim: To calculate the value of a deposit of gold to a guild bank (gbank) that discounts sales at a given rate.

Summary:
  • A donation of G gold to a gbank with a decimal discount rate of r will be worth G/r gold. This means that G is multiplied by 1/r, the reciprocal of the discount rate. Keep in mind that Full price = Discounted price + Discount.
  • As long as the discount rate is less than 100%, the donation is worth more than the amount donated (even in pure money terms)!
  • A gbank donation's impact will grow according to the sum of a geometric series and approach a limiting value.

The given:
  • The discount rate is fixed.
  • There is no cost in performing transactions and the full proceeds of a gbank sale are deposited back in.
  • All gold is used in buying other resources for resale. No gold is dispensed as a repair allowance (though it can be factored into the discount rate).

The detail:
Consider a gbank deposit of G gold. It is used in buying (for example) enchanting materials worth G gold. They are sold to a guild member at a discount rate of r, so the undiscounted proportion of the price is:
1 - r

The proceeds from that sale are:
G × (1 - r) = G(1 - r) gold

The proceeds are then used for buying potions worth G(1 - r) gold. There potions are sold at a discounted price of:
G(1 - r) × (1 - r) = G(1 - r)2 gold

Continuing this process for n terms, we get the following progression of values:
G, G(1 - r), G(1 - r)2, G(1 - r)3, ... , G(1 - r)n - 1

The geometric series 1 + 1/2 + 1/4 + ... , with its value represented by area.

This is in fact a geometric progression with common ratio (1 - r) and first term B. Note that, while the amount deposited diminishes, it keeps making an impact with each gbank sale. The total impact for n sales is the following sum of the corresponding geometric series:
S(n) = G(1 - (1 - r)n) ÷ (1 - (1 - r)) = G(1 - (1 - r)n)/r gold

As n » , (1 - r)n » 0 , and (1 - (1 - r)n) » 1 . So, the total impact approaches the following limiting value as resales are conducted repeatedly with that amount:
S() = G/r gold

Here is an example. Say 100 gold is donated to a gbank with a discount rate of 25% or 1/4. That donation will be worth:
100 ÷ 1/4 = 100 × 4 = 400 gold

15 July 2009

How Hitler became Chancellor and Führer

Since Adolf Hitler is a strongly condemned political leader, the circumstances around his rise to power are very interesting. Germany's desperation post-World War I, the Great Depression, hyperinflation and emerging communism promoted this process.

Suffering after WWI
WWI ended when the Treaty of Versailles was signed. In it, the Allied countries required Germany to pay war reparations, surrender territory and reduce the power of its defence forces. These provisions (along with a declaration to surrender) were a large blow to Germany's national pride. Also, the indecisiveness of the democratic Weimar Republic meant that laws took a long time to be passed.


This 1000 Reichsmark note was overstamped to a face value of 1 000 000 000 Reichsmark.

The German economy suffered in two ways during some of this period. The country was required to pay currency as part of its reparations, which was financed substantially by printing extra currency. This caused hyperinflation of the Reichsmark, even during the Great Depression following the US stock market crash. Face values fell well below the cost of the paper, leading to (among other things) persons' burning it as firewood during famine winters. Even though it ended after three years (with the introduction of the Rentenmark), a lack of popular confidence was cast on the financial system (substantially comprised of Jews).

Enter Hitler

Hitler's DAP (predecessor to the Nazi Party) membership card.

Seeking participation in politics, Hitler joined the German Workers' Party (progressing to the NSDAP or Nazi Party), which was notably far-right in the political spectrum. It promoted (among other things) nationalism, anti-communism, economic recovery and abandoning the Treaty (though the anti-Semitism can be observed in the rhetoric). He possessed a demonstrated charisma and easily appealed to most of Germany's citizens. Hitler eventually became the sole leader of the party.

The following circumstances existed for the Weimar Republic:
  • The system of government at this time was parliamentary republic under constitution, which made for several political parties to contend for the popular vote. In it, there was a President (elected by popular vote) who ceremonially signed bills into law, and a Chancellor (approved by parliament after nomination by the President) who led the party in government.
  • The Weimar Constitution codified civil liberties such as habeas corpus (freedom from unlawful detainment), freedom of expression, freedom of association, privacy of telecommunication and protection of property and home.
  • The Weimar Constitution allowed the President to issue decrees (which did not need parliamentary approval) in times of emergency.
  • The Weimar Constitution placed limits on the laws that can be made, and any deviation was considered a constitutional amendment requiring a two-thirds majority in the Reichstag parliament.

The fire at the Reichstag
Das Andere Deutschland was rendered verbot (forbidden) under the Reichstag Fire Decree.

On January 1933, Hitler was sworn in as Chancellor after nomination by President Paul von Hindenburg. A month later, a fire occurred in the Reichstag building. Communist Marinus van der Lubbe was found inside after the fire was extinguished, which the Nazi Party used as evidence of a Communist uprising. President von Hindenburg signed the Reichstag Fire Decree into law a day later, which allowed the beforementioned civil liberties to be suspended, so as to quickly arrest communists suspected to be involved and ban the Communist Party. However, Hitler (being head of the executive) also used the Decree to arrest anyone and suppress any publication deemed unfriendly to Nazi ideology.

Enabling Hitler to act

Hitler (wearing light clothing) presents his speech promoting the Enabling Act.

The Nazi Party started drafting an Enabling Act on March 1933, which would allow them to pass laws without needing it to go through the parliamentary process (as required by the Constitution). However, because it would allow deviation from the Constitution, it needed to be passed with a two-thirds majority as an amendment. On voting on the bill later in the month, support was won to achieve the majority, with the Communist Party banned at the time and the Social Democratic Party the only party to vote against it.

The perfect storm
The German people wanted the former glory of their nation to be restored. A communist happened to be found in the burnt Reichstag building. The Decree suspended several basic civil liberties, while the Enabling Act diminished the importance of the parliamentary process. Both could be renewed when close to expiry. Hitler was the sole leader of the Nazi Party and could wield both instruments as a dictator. The senile President von Hindenburg seeked minimal participation in politics, and when he passed, Hitler assumed his powers. It comes to little surprise that Hitler's rise to power was entirely legal and compatible with popular German opinion (however much it contained desperation).


A chocolate model of the Reichstag building, which would have melted under fire.

13 July 2009

The Spectrum of Classes


This spectrum diagram illustrates the position of WoW's nine playable classes in the class balance. It is two-dimensional: rigour is read along the horizontal axis, while tactic is read along the vertical axis.

Rigour: Any given class uses a certain balance of physical abilities (using a weapon and/or shield) and magical abilities (casting spells) in combat. The classes to the right place an emphasis on the magical, with the priest and mage being magically pure. Classes closer to the centre are hybrids, who appreciate a combination of the magical and physical. The druid enjoys most a balance of the two rigours. The mana line divides the spectrum into those who use mana and those who use other power sources. To the left are the classes who place emphasis on the physical, with the warrior and rogue being physically pure and to the left of the mana line. Hybrid classes near the centre can tweak their respective balances through talent specialisation, though pure classes at the extremes are resolute about their respective masteries.

Tactic: Any given class uses a certain balance of tenacity and ferocity when engaging in combat. Tenacious classes will mitigate the damage taken in an attempt to outlast the opponent. The tenacious warrior will reduce the damage taken initially through heavy armour, while the tenacious priest will heal the damage that is taken. Ferocious classes maximise damage dealt to end combat as soon as possible. The rogue and mage place emphasis on this. Tactic can be tweaked by all classes through talent specialisation. The classes at the junctions (warlock and hunter) enjoy the versatility that class pets bring, so as to exercise a level of control over this balance.

It would be important to note that I cannot find a place for the new death knight class in this spectrum. This may be due to the youth in their class development; Blizzard simply has not yet found a niche that they can fill. It may suggest any of the following:
  1. There are no more niches that a death knight (and future hero classes) can fill, and they are doomed to be patchworks of any of the nine original classes. In fact, death knights possess some of the qualities of paladins and warlocks.
  2. The domain of the death knight and other hero classes lies outside of this spectrum.

10 July 2009

Flagging for PvE

WoW's PvP flag is a game mechanic introduced in its earliest days, where it marks the player for player-versus-player (PvP) activity. While very simple, it also has ramifications on the player's experience of player-versus-environment (PvE) content. Needless to say, the flag does not need to be permanently up for a PvE raid.

In fact, the PvP flag should not be permanently up for a PvE raid. Patch 2.4.3 introduced the following change:
Zoning into an instance on a PvE realm will now drop your PvP flag.

The game approaches flaggable actions conservatively. While targeted attacks towards enemy players or targeted aid towards PvP-flagged friendly players will raise the flag, incidental attacks or aid will not. This means that:
  • Area-of-effect (AoE) heals (e.g. Prayer of Healing) cast by an unflagged healer will not affect flagged players, unless the flagged player was targeted on spell cast.
  • Raid-wide buffs (e.g. Prayer of Fortitude) cast by an unflagged buffer will not affect flagged players.
  • Healing a flagged player flags the healer.
  • Buffing a flagged player flags the buffer.

It would be safe to assume that a majority of players disable PvP. It is therefore best that, for a PvE raid on a PvE realm, any permanently raised PvP flag should be lowered! This is done though the player's portrait's drop-down menu shown above.

There is yet another important note for PvP flags. Many PvP quests written into the Quest Log will keep the flag up until completed or abandoned. If the flag stays up 5 minutes after disabling PvP, this may be why.

07 July 2009

Random Ramblings to 7 July 2009

Biomolecule
A molecule that can be produced by any organism. As would be expected, they make up much of the mass of organisms. The ones used in building a cell are glycerides (making up lipids (such as fat)), nucleotides (making up DNA and RNA), amino acids (making up proteins) and saccharides (making up carbohydrates).


Sucrose, a disaccharide biomolecule found in table sugar.

Network effect
A concept in economics that describes how certain goods or services become more useful the more consumers there are consuming it. Examples include operating system software (which allow greater compatibility between computer systems) and social networking facilities (where a single consumer can meet more people where more consumers are using it).

Queen's Counsel (QC)
Barristers in Australia are lawyers who specialise in presenting cases to courts. QC is the rank of barrister higher than junior and lower than Senior Counsel (SC). They are well known for their superior expertise in presenting such cases and the exorbitant fees they charge for this privilege.

Random number generator
Program code which allows a random numerical value to be generated. It is commonly used in programs to process instructions in random ways. In WoW, a /roll slash command runs the RNG to produce a random integer between 1 and 100. I use the phrase "Lady RNG" to evoke the concept of Lady Luck.

Scanning system (of a display)
A display's screen consists of a grid of cells (pixels), where each pixel's light output can be individually changed. The display would change each pixel by scanning from left to right on a single line, then from the top line down. An interlaced scan would scan alternating lines over two passes to render a full frame. A progressive scan would scan all lines in one pass. While interlaced scanning requires less information to render a moving picture (since only half of the frame is rendered in a pass), progressive scanning avoids interline twitter (where otherwise still objects seem to jiggle up and down). The i in 1080i implies that the scanning system used is interlace, while the p in 1080p implies that the scanning system used is progressive.

Stare decisis
The doctrine of precedent in as followed by courts. It translates from Latin to "to follow previous decisions". Under this legal principle, courts are normally required to apply the details of previous court cases to the current case if the facts involved are sufficiently similar. This provides for predictability for court rulings, but (by itself) does not allow judge-made law to change in accordance with changing values held by society.

(DSL line) Synchronisation
When a DSL modem is connected to a line, its clock is initially out of sync with the clock of the DSLAM upstream. Line synchronisation is the process through which each offset their clocks so their rhythms coincide with each other. The rhythm is needed for both the modem and AM to send and receive signals properly, since the electrical pulses are to be slotted in between the regular beats. During this process, the quality of the line is also checked. Line sync is the status of when the two are properly synchronised. Line sync can be lost when excessive interference enters the line.


The regime of a DSL internet connection.

Theobromine
An alkaloid substance which is most commonly found in cocoa and chocolate, having the chemical formula C7H8N4O2. It does not contain any bromine, but rather is named after the scientific name for the cacao plant (Theobroma cacao, of which the genus is Greek for 'food of the gods'). As is can be produced when caffeine is decomposed, it is a stimulant drug (increasing nervous system activity). It is infamous for causing poisoning in animals (in particular dogs) because they cannot digest it as fast as humans can.


A stack of chocolate pieces. The brown ones contain theobromine.

06 July 2009

The Clock-cycle Model of Chain Casting

Chain casting is an action where multiple spells are cast in succession with minimal delay between them. This is a crucial skill in raiding, where (provided that the person does not upset a mob's threat table) it improves individual performance, whether tanking, healing or dealing damage.

There are striking similarities between how one chain casts and how a computer's processor works. The following will draw parallels between the two, and may allow the chain casting process to be treated differently to frantic button-mashing. It would be important to know that the central processing unit (CPU) is the component of a computer that follows a series of instructions to produce a series of results. Only spells with cast times of some multiple of the global cooldown will be considered.

Processing an instruction <--> Spell casting
The instruction (in computing) is the atomic unit of a CPU's entire workload. the CPU can only digest one instruction at a time (though if it has n cores, it can process n instructions at the same time), and will do so in sequence.

When casting a spell, the player selects a target, decides which spell to cast and presses the appropriate button (in any order). The player does this repeatedly and sequentially while chain casting.

Clock generator <--> Global cooldown
A crystal oscillator which can provide a clock signal to a computer system.

By itself, the CPU has no concept of time and thus cannot process instructions (which take time). A clock generator provides a rhythm (the clock signal) to the CPU. As a certain amount of time passes between beats (clock cycles), the CPU can use this rhythm to perceive time. It will then process however many needed instructions in a clock cycle (or vice versa). The frequency of the clock generator is measured in hertz (Hz), or cycles per second.

The global cooldown (GCd) is the minimum time that needs to pass between spell casts, which (when not modified by Haste Rating or Bloodlust/Heroism) is 1.5 seconds. This corresponds to a frequency of 2/3 Hz. (As a side note, Haste Rating can reduce the GCd to 1 second and increase the frequency to 1Hz.) This GCd can provide a rhythm which avoids the need for button-mashing. Some long-cast spells (e.g. Greater Heal) take whole multiples of one GCd to cast, which can be spread over several multiples without losing the sense of rhythm (simply miss a few beats).

Clock multiplier <--> Chain casting ability

An interface showing a system's system clock settings.

The clock multiplier multiplies the clock rate by a certain number n, so that the clock signal actually used by the CPU is n times faster than the clock signal from the clock generator.

A novice player may be able to cast 1.5 second spells over 3 GCds (frequency of 2/9 Hz), which, if the GCd was used for the 'clock signal', would cast on a 'clock multiplier' of ~0.33.

Overclocking and resulting overheating <--> Practice and resulting fatigue
Overclocking the CPU involves setting its clock multiplier higher. This hastens the clock signal in use and causes the CPU to work faster. However, by working faster, the CPU also generates more heat. If it cannot withstand the heat, it will start introducing errors in its work.

With practice, the player can chain cast close to the maximum 'clock multiplier' of 1. However, if they keep this up, they will get tired (if done repeatedly, they may suffer burnout). In normal raiding, the practical maximum is not usually needed, and the player can afford to work suboptimally to keep their energy levels up.

Interrupt handling <--> Situational awareness
A (software) interrupt is an instruction for the CPU to stop processing a set of instructions (a process) and start processing another. It allows a single CPU to run several processes at the same time (multitask) by simply switching between them.

Raid encounters rarely involve simply casting spells at fast as possible. There are almost always random events to respond to. The player would chain cast as normal, then interrupt it to respond promptly to events needing attention. For example, a tank healer responsible for two or more tanks would need to switch constantly between them, devoting most of their attention to the target tank. Some attention would be reserved for recognising the healing needs of the other tank(s), as well as responding to the environment.

Something to consider
A Brunel University study found that working to a rhythm reduces fatigue. By casting in time with the GCd (or some other rhythm), less energy will be used and the player will be able to more easily sustain their performance in a raid.

01 July 2009

Playing the Blame Game

For many frustrated raiding groups, there are boss NPC encounters that stump them so many times. Those bosses might allow only a small margin of error; no matter how much knowledge and experience those players possess, a simple mistake made by any of them can snowball into a wipe. While still existing in all encounters, it is these ones that causation is most evident.

Simply, causation is the relationship between an event and its effect, such that the event causes the effect. Using this concept while diagnosing a raid wipe, the effect of the wipe can be credited to the event of a particular person's (or persons') misconduct (and therefore can be identified as something to avoid next attempt) if a causal relationship can be established.

Consider the following...
To demonstrate this type of troubleshooting, I will use a theoretic (though still plausible) attempt under the Archimonde encounter in the Battle for Mount Hyjal raid, the encounter in which causation may be the most evident. It would be important to note that, at level 70, the typical nontank health is ~7500. Archimonde has the following abilities:

Consider the following plausible scenario, where A is Archimonde, B and C are dps, H is a tank healer and T is the tank:
A casts Air Burst on B. B fails to break their fall (using Tears or otherwise) and dies from fall damage. Archimonde gains a Soul Charge (the silencing sort), which he immediately uses and cuts every nontanks' health by half. A then inflicts H with Grip, which C, who is the only curse dispeller in range, cannot dispel under the silence. A then casts Fear, making H run out of range of C into a Doomfire. H cannot heal through this much damage and dies. T is left vulnerable and A gains another Soul Charge. A uses it and kills both T and all melee dps. A starts spamming Finger of Death, eventually leading to a wipe.

Follies in diagnosing the raid wipe
The raid, diagnosing this wipe, would reasonably ignore all events after the tank's death and attribute the fault to the healer, who caused T's death by insufficient healing. (In the extreme case, T would be blamed for the wipe because they died!) Unfortunately, doing only this will not provide a full picture of the attempt. The insufficent healing was under extenuating circumstances, after all!

Diagnosing the raid wipe by buck passing

A buck and a set of playing cards used in poker.

H is now said to hold the buck. If H can attribute their fault to someone else's fault through causation, they are said to pass the buck, with such an action being called buck passing. Under buck passing between players, the buck will ultimately stop at a single player or group of people, who can be deemed ultimately at fault.

It would important to note that the effect of a preceding event is also the event of the succeeding effect. The following series of events can be constructed from the scenario, ordered according to reverse chronology and linked by causation:

  1. There is no one in melee range alive after the second Soul Charge and, after A's spamming Finger of Death, the raid wipes.
  2. T fails to receive sufficient healing and dies.
  3. H suffers unhealable Grip and Doomfire damage and dies.
  4. C is silenced from the Soul Charge and H is Feared out of range, so C cannot dispel H's Grip.
  5. B fails to break their fall when A casts Air Burst on them and dies, earning A a Soul Charge.

From this, the following series of causation can be derived:
  1. The raid wiped because the T was dead and not reducing A's damage to the raid in general.
  2. T was dead and not reducing A's damage to the raid in general because H was dead and not healing.
  3. H was dead and not healing because H suffered unhealable damage from Grip and Doomfire, which would have been healable if C dispelled Grip.
  4. H suffered unhealable damage from Grip and Doomfire, which would have been healable if C dispelled Grip, because C was silenced by the Soul Charge from B's death, and by the time C could cast spells again, H was feared out of range.
  5. C was silenced by the Soul Charge from B's death, and by the time C could cast spells again, H was feared out of range because ...



The series of events and causation can be merged into a chain of fault, which allows for a buck to be passed along it. By the time the diagnosis reaches point 5., the buck would have stopped at B, where B cannot blame anyone else. Here is where the ultimate fault rests, because if it were not for this player's action, the whole chain of events would not have happened! The raid would then consider this something to learn from and maybe would even discipline the player at ultimate fault.

Junctions of preceding causations
Could anyone along the series of events have introduced their own fault along the way, continuing the chain of events? If they did not introduce the fault, could the chain of events have terminated? Certainly (e.g. considering event 4., if C did not notice a 0.5 sec window of opportunity to dispel the curse from a H barely in range), but these can be ignored for any of the following reasons:
    • The preceding causation would have made it unreasonable for this person to have acted properly, e.g. if C was too distracted at considering the Soul Charge that they did not notice said window of opportunity.
    • A properly established causation can make said fault insignificant, and the chain of events would proceed the same way even if it did not exist.
    • For all practical purposes, the possible said fault is unlikely to happen. Whether it actually does is out of the scope of ordinary World of Warcraft raiding and can (depending on disposition) be predicted by divination or actuarial science.
    What if a proper causation holds yet the extra fault stays significant, if both (or more) were required for the series of events to continue? For example, considering event 3., there was in fact a second healer nearby (named J) which made the damage unhealable because they were not healing H? 3. then becomes a junction of two preceding causations: had C dispelled H's curse, J's healing would not have been needed, and had J healed H, C's dispel would not have been needed (at least for the meantime). Here, the buck splits into two, and they are passed up two separate branches of series of causation: while the raid figures out why Grip was not dispelled, they are, at the same time, figuring out why J was not healing H. The chain of fault then becomes a tree of fault.

    Groups at fault
    Consider causation 5. Say that B, while Air Bursted, was whispered to by another player D who was warning them (at the very last minute!) that they were airborne. This whisper distracted B so B ended up not interrupting their fall. There is then this following segment of the chain of events:
    1. B fails to break their fall when A casts Air Burst on them and dies, earning A a Soul Charge.
    2. D whispers to B about the Air Burst and B becomes distracted.
    There is then the following chain of causation:
    1. B fails to break their fall when A casts Air Burst on them and dies, earning A a Soul Charge because D whispered B about the Air Burst, distracting B from breaking their fall.
    2. D whispered B about the Air Burst, distracting B from breaking their fall because D anticipated B to fail to break their fall when A casts Air Burst on them and die, earning A a Soul Charge.
    3. B, as a matter of fact, fails to break their fall when A casts Air Burst on them and dies, earning A a Soul Charge because D whispered B about the Air Burst, distracting B from breaking their fall.
    4. D whispered B about the Air Burst, distracting B from breaking their fall because D anticipated B to fail to break their fall when A casts Air Burst on them and die, earning A a Soul Charge.
    5. B, as a matter of fact, fails to break their fall when A casts Air Burst on them and dies, earning A a Soul Charge because D whispered B about the Air Burst, distracting B from breaking their fall.
    6. etc...
    In this case, the buck is endlessly passed between B and D! This signifies that a group of people are at ultimate fault, where the faults of these people (in this case, B's and D's) are mutually dependent on each other. This is despite that the chain of events does have a definite beginning. Inspecting the series of events overall, it can be observed that if this group had not been at fault, the whole series of events would not have occurred! The raid would then consider this something to learn from and maybe would even discipline the group at ultimate fault.

    Of course, another person or group could have caused said group to be at fault; the group does not need to be at ultimate fault. This would extend the chain of fault further.

    Methodology
    The person or group at ultimate fault is the person/group who started the chain of events, and had they not done so, the chain of events as it is known to have occurred would not have existed. To find this person/group under buck passing:
    1. Construct a series of events from the wipe backwards. Each event should involve a single player's actions that make them at fault, and should exclude any actions beyond player control (e.g. the boss' behaviour).
    2. Construct a series of causation, connecting events together using "because" or "causes". Note where (if at all) the buck seems to pass between the same people and deal with it (no pun intended) accordingly.
    3. Merge the series of events and series of causation into a chain of fault. Analyse for any junctions (where an event joins several preceding causations) and groups at fault (where members are blaming on each other) and amend the chain of fault accordingly.
    4. Pass the buck up the chain of fault. Where the buck(s) stop(s), the person(s)/group(s) holding it/them are deemed to be at ultimate fault.

    30 June 2009

    Writing Cheques

    A cheque is a written instruction by a person (the drawer) to their bank (or other financial institution) (the drawee) to pay cash to another person (the payee). It must not be subject to any conditions. While cheques are not commonly used these days, many drawers still enjoy the delay in its clearance if they consider the payee suspicious.

    There are several markings made on a cheque, which essentially answer the following questions:
    1. Should the cheque be cashable by any bearer of the cheque, or only by the payee named on it?
    2. Should the cheque be able to be redeemable in cash at the bank counter, or should it be credited to a bank account?
    3. Does the payee want to make the cheque payable to another person?
    4. Should 3. be allowed to happen?

    1. Bearer and Order cheques
    • If a cheque is payable to bearer, the person who presents it to the bank counter can cash it for themself, regardless of who is named payee on it. A bearer cheque will have the words "or bearer" or no such additional words printed on it, such that, if the payee is named A.B., the instruction reads "Pay A.B. or bearer", "Pay cash or bearer" or "Pay cash".
    • If a cheque is payable to order, only the payee has rights to cash the cheque. An order cheque will have the words "or order" or "to the order of" printed on it, such that the instruction reads "Pay A.B. or order" or "Pay to the order of A.B.".
    • A bearer cheque can be made payable to order by crossing out the words "or bearer", such that it reads "Pay A.B.". An order cheque can be made payable to bearer by not stating a name or making it payable to either "cash" or a fictitious person (e.g. "I love you"). The instruction for the 2nd case would read "Pay cash or order".

    2. Cheque crossings
    A cheque is crossed when two parallel lines are drawn along the cheque's face. Doing this means that the cheque cannot be redeemed in cash at the bank counter, and so must be credited to a bank account. If the cheque is not crossed, it becomes redeemable in cash.

    3. Indorsements
    For a cheque payable to order, the payee (acting as transferor) indorses the cheque when they write instructions on the cheque to make it payable to another person (the transferee). If the transferee is named X.Y., it would read "Pay X.Y. {signed} A.B.". Since a cheque payable to bearer can be cashed by anyone, there is no need for any indorsement for them.

    4. /NOT NEGOTIABLE/
    A bearer cheque is crossed 'not negotiable' when the words "NOT NEGOTIABLE" are written between the parallel lines. Most importantly, this means that the payee will not be able to indorse the cheque. However, this also means that, if the bearer stole the cheque from another person, they do not have ownership rights to the cash. Both of these cases mean that:

    • The bank is not obliged to cash the cheque for the bearer.
    • If the bank cashes the cheque, the drawer suffers a loss and they can sue the bank for related damages.

    Also...
    "Cash" is not a true entity, but rather it signifies that the cheque should be payable to bearer. It may be baffling, but solace can be taken in the instruction's making grammatical sense.

    It is interesting to note that any marking made reduces the rights of other persons to cash the cheque. For example, if "or bearer" is crossed out in a bearer cheque, it becomes payable only to the named payee, while a similar marking over "or order" in an order cheque keeps it an order cheque payable only to the named payee. When a marking is made (presumably in pen), the only way to void it is for the drawer to cross it out and sign it off. These schemes support the nemo dat rule:
    Latin: nemo dat quod non habet
    English: no person can pass a better title than they possess

    27 June 2009

    The Origin of (Warcraft) Species

    No fantasy universe is complete without an evolutionary history of all of its living (and unliving) races. In the case of Warcraft, this is not at all uninteresting. All deviations from common ancestors can be explained in one word: corruption.

    I will give a brief account of the player races of Azeroth in three logical sections, grouped according to three unique circumstances. These are:
    1. The Seed Races, as created by the Titans;
    2. Aliens, which more or less were introduced into the Azerothian environment;
    3. The long-eared and bovine races, whose ultimate origins are not recorded by any surviving written sources.

    The Seed Races


    When the Lord God made the universe, there were no plants on the earth and no seeds had sprouted, because he had not sent any rain, and there was no one to cultivate the land...

    Then the Lord God took some soil from the ground and formed a man out of it; he breathed life-giving breath into its nostrils and the man began to live.

    Then the Lord God planted a garden in Eden, in the East, and there he put the man he had formed. He made all kinds of beautiful trees grow there and produce good fruit.

    Genesis 2:7-9, GNT

    Azeroth as it (mostly) is today started with the Ordering thereof. During this period, the Titans began shaping the natural features of a then chaotic world. At the same time, they created three so-called "Seed Races" from living stone, to inhabit the world: earthen, vrykul and giant. As they were made of stone, they were (in the Warcraft meaning of the word) immortal. In shaping Azeroth, the Titans encountered the Old Gods, who were innately evil and symbiotically attached to this world. In destroying the Old Gods, the Titans would also destroy Azeroth, so they were forced to imprison them deep below the surface.


    The "matrix" of nucleotide building blocks in DNA.

    However, the Old Gods were able to propagate the Curse of Flesh, a "matrix destabilisation". In effect, it softened many of the Seed Races, shortening their lifespans dramatically and rendering them mortal. In creating the earthen, the Titans went through three iterations. The Series One experiments were a failure, not only because the resulting form was well short of ideal, it also succumbed to the Curse. This species is currently known as the troggs. The Series Two experiments produced the intended form (that of the dwarves), but the results were still susceptible. The Titans succeeded with their goals with Series Three, giving birth to earthen proper. The earthen were able to withstand the Curse, and stay stone-like to the present.

    There was only one iteration of the vrykul, which succumbed to the Curse. They survive to this day.

    At some time after the Pantheon (the ruling council of the Titans) left Azeroth, Vrykul mothers gave birth to children who were noticeably smaller and physically weaker than normal. King Ymiron (vrykul society's head of state) ordered them culled, but many mothers opted to abandon them instead. These children were shipped off to the Eastern Kingdoms (they were inhabiting Northrend), where they developed as humans.

    Throughout Warcraft history, the Burning Legion (a demonic nation) have been trying to conquer Azeroth. In their third bid, their Supreme Commander Kil'jaeden converted the orc warlock Ner'zhul into the Lich King and tasked him with concocting a Plague of Undeath to (among others) be spread among the citizens of Lordaeron. Ner'zhul was successful, and was able to task Kel'thuzad with transporting it to the Eastern Kingdoms. There, Kel'thuzad formed the Cult of the Damned out of oppressed Lordaeron citizens and tasked them with propagating the Plague. It would kill the infected after a typical three days, then raise them as undead beings. These would do the bidding of the Lich King, as they had lost their free will in the raising process. The playable Forsaken undead regained their free will after a Nathrezim (dreadlord) raid on Lordaeron, which somewhat waned the hold of the Lich King over many of the undead.

    The giants were created by the Aesir (storm giant) Titans to help with shaping Azeroth during the Ordering and when the Titans left. The direct creations were the mountain and sea giants, who were respectively tasked with shaping mountains and seas. From the mountain giants developed the frost giants. The giants have mostly resisted the effects from the Curse of Flesh, though Archavon the Stone Watcher reports having felt a soft face on himself.

    The origins of the mechagnomes are currently unknown, though most have felt the destabilising effects of the Curse. These mechagnomes developed into the current gnomes. However, Gearmaster Mechazod found a way to cure affected gnomes of this Curse, effectively returning them to their robotic selves. Most gnomes would refuse this cure.

    The Aliens

    The eredar race originally lived on the planet Argus. However, Sargeras, a formerly Vanir (earth giant) Titan, was seeing a folly in the Pantheon's ways and started forming the Burning Legion to reverse their work. He offered the three eredar leaders (Archimonde, Kil'jaeden and Velen) great power in exchange for their loyalty. The former two accepted, and as a result much of eredar society transformed into the man'ari eredar, who joined the Burning Legion. Archie and KJ became high-ranking officers in it.

    Velen, being a prophet, foresaw horrid visions of the Legion's actions, and as a result was inclined against joining. Naturally, for conflict-of-interest reasons, Velen and the uncorrupted eredar under his care were forced to flee Argus and was chased throughout the Twisting Nether, hopping worlds until they managed to find the secluded Draenor. There, they developed into the draenei and coexisted with the native orcs.

    The Legion eventually found the draenei in Draenor. They introduced warlock magic to the orcs after appealing to them and their leader the then-shaman Ner'zhul. Orcs originally have brown skin, but exposure to such demonic magics will turn it green. This will occur even in orcs that do not practice such magic but are in regular proximity to practitioners.

    The Mag'har section of orc society remained untouched by corrupting fel energy. They lived in Garadar, which was originally intended as isolation from the red pox outbreak pre-dating the arrival of the Legion. Nonetheless, it also isolated these orcs from practising warlocks, and their skin remains brown to the present.

    The draenei fled again from Draenor, though some opted to stay behind. These draenei were particularly susceptible to demonic corruption, and many degenerated into the Broken and Lost Ones.

    Some orcs have also been drinking the corrupting blood of the pit lord Magtheridon. over time, this turns them into the current fel orcs, characterised by great physical strength, red skin and all manner of protrusions.

    The long-eared and bovine races

    The Zandalari trolls existed since the beginning of the world, though their creation is unknown. As troll society expanded, trolls started inhabiting different climates, eventually adapting to their respective environments. The ice trolls living in Northrend developed pale blue skin and hardy hair. The sand trolls living in Tanaris developed golden-yellow, coarse skin. The skin of forest trolls living in Lordaeron is able to support plant life. The skin of jungle trolls (of which the playable Darkspear trolls are part) is covered with nice, soft fur (they would be very nice to hug!) which produces a purple appearance.

    At the centre of pre-Sundering Azeroth lay a huge inland ocean called the Well of Eternity. It radiated arcane energy from the Twisting Nether and nourished all natural life. The night elves had developed on its shores, and there is a controversial theory that the Well's energies caused them to mutate from trolls. Nevertheless, the high elves are those night elves who utilised the Well's power in arcane magic. Abuse of such led to the Great Sundering, which tore the single continent into Kalimdor and the Eastern Kingdoms and destroyed the Well of Eternity. Arcane magic being addictive, the high elves developed peach-coloured skin. The playable blood elves are those high elves that, instead of fighting the addiction, chose to continue gorging themselves with arcane, demonic and holy satisfaction.

    Some high elves were thrusted deep into the ocean during the Great Sundering. While some drowned, Queen Azshara secured an agreement with the Old Gods which allowed many to survive without air. These high elves became the naga.

    The tauren and taunka are ancient races existing before recorded history. They are believed to have been created by the Earth Mother. However, there are theories equating the Earth Mother to the night elf god Elune, Therazane the Stonemother, Alexstrasza the Life-Binder (leading the Dragon Aspects), the Vanir Titan Eonar the Lifebinder and the Titans in general.