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  1. #1

    King Doric's Progeny: A Mathematical Exploration for Guild Wars

    Caveat: The idea presented below is merely a fun exploration in basic mathematical modeling, designed to bring about further depth into an amazing on-line experience. However inaccurate or improbable it may be to some, remember that this is in no way meant to be a definitive source of knowledge for Guild Wars. Enjoy.

    Well, up until now, I always wondered when I would cross that special threshold between pseudo-nerd and that coveted title that all strive for. But today, I have achieved the impossible with this act. Some of you may have heard some time ago about a recent anthropological study that linked approximately 3 million male individuals world wide to Niall of the Nine Hostages, a sixth century Irish king mentioned in the lore regarding St. Patrick. Niall had twelve sons and as a result of his reproductive success, he is now regarded as the most prolific Irishman of all time.

    Now the question that I pondered on is this: One of the central tenets of Guild Wars lore is the fact that all the Chosen are descendants of King Doric, the first monarch of the humans. If we, in the real world were able to link 3 million men to one common ancestor, could it not be possible to calculate how many Chosen would most likely be alive during the time period of the Guild Wars game. I became so enthralled in the idea that I actually decided to put my calculus skills to some use.

    I started out by first examining and basing a mathematical model on the proliferation of Niallís descendents. To do so, I used a basic exponential growth equation A = Aoekt, where A represented final amount, Ao was the initial amount of children (in this case, only sons because the Niall study traced lineage via the Y chromosome), e is the mathematical constant represented by the letter e ( 2.718281828Ö.), k is the exponential constant, and t is the time in years over which the growth occurred. So using this model, we have the final amount for Niallís children as A = 3 million, the initial amount of children, Ao, equals 12, e is constant, k is unknown, and t equals 1,700 years. Therefore, our equation is set up as:

    3,000,000 = 12e1700k

    I then solved for k by dividing by 12, and then took the natural log (ln) of both sides:

    Ln(250,000) = ln(e1700k)

    I bring down the exponential, which is a property of logs,

    Ln(250,000) = (1700k)*ln(e)

    And then drop ln(e) because it equals 1,

    Ln(250,000) = 1700k

    I finished the problem by dividing both sides of the equation by 1700 to receive a constant of:

    0.0073113036 = k.

    With this constant, I then attempted to apply it to Doricís line. I made several assumptions in using this equation: First, I assumed that Doric had the same number of children as Niall did judging that their societies were probably the same in terms of kings producing larger numbers of surviving offspring than common folk, so Ao equals twelve. I also assumed that there would be no abnormalities in the reproductive success of his descendants (i.e. No one offspring sired an absurd number of children and no one line died off). The last assumption comes in regard to the time period over which Doricís line had time to proliferate. Assuming that the starting point came approximately around the Exodus (0 A.E.), I then established that the overall time period for which Doricís offspring could multiply was 1,070 years, the time between the Exodus and the start of the game. So using the model I had established, the equation written out appeared like this:

    12e0.0073113036(1072) = ?

    The final solution came out as:

    29,972 male individuals from Doricís line were alive at the start of the story.

    Double this result by assuming that for every male descendant there is a female counterpart, and you have a total of 59,944 offspring of King Doricís line at the start of the game.

    Now I must make a few disclaimers before I conclude this discussion. I am in no way a math major. I simply took a basic calculus formula and applied it to an area of interest. Furthermore, liberty in regard to numerical values were taken due to a lack of data regarding the number of children Doric actually had, simply because Anet probably never foresaw that anyone would be crazy enough to try this. In addition, as I previously stated, I did not take into consideration abnormalities in the proliferation of Doricís children, because it is a simple model with little ground in the real world, and I lack the expertise and know how to develop a better one. I should also note that the number of Chosen probably dropped dramatically, as a result of the Searing and Cataclysm that reeked havoc on the populations of Ascalon and Orr, so my calculations cannot account for this. Finally, this investigation was done for fun and is in no way attempting to disguise itself as numerical fact or canon.

    Now what does this information imply? First off, it gives us a way of viewing the actual size and scope of Tyriaís human population. Of course, in the game, the number of NPCs is scarce in relation to the number of players, but that is a limitation of the game to match a real human society, and not the actual population of the world. Therefore, we can safely assume a minimum ratio along the line of maybe 20 common people for every Chosen. Again, this is a random number being used for illustrative purposes. This would bring the Tyrian human population up to about 1,198,880, a reasonable number considering the size of the continent and the level of culture that has developed.

    Another implication of this data is in regard to the Mursaatís use of the Bloodstones. The Mursaat sacrifice the Chosen in order to use the Chosensí souls to power the magical seals on the Door of Khomalie. If the number of Chosen were only a few hundred, then the Mursaat would have killed them off too quickly to make any use of the Chosen as a stable power source for the Door. Therefore, this could even mean that the Mursaat allow the Chosen to multiply, full knowing that they walked a dangerous line in cultivating a resource that one day may rise up to destroy them.

    The final implication that Iíll make is simply this: Guild Wars has a user base that I think now has reached close to 1 million. According to my calculation, possibly 60,000 inhabitants of Tyria are actually Chosen. Therefore, in agreement with my logic and data, I can only conclude this: A lot of people are faking their birth certificates.

    I hope you enjoyed reading this exploration in mathematical examinations of GW. Feel free to double check my steps and critique any statement I make that could be countered in the official lore. I might have missed something that alters the end-result of my calculations. Thank you for reading, and have a good day.

  2. #2
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    Dude, ya nuts. We could use more people like you!

    I enjoyed reading your article and your calcuations seems plausible to me. Of course there would be more than handful Chosen out there

  3. #3
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    Good work, I quite enjoyed reading your research and to me, the math seems sound enough.

  4. #4
    Thank you both for the compliment. I was a little worried in posting this, but now feel glad that I could contribute in some way.

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    Quote Originally Posted by Sgilti Lightfoot
    Thank you both for the compliment. I was a little worried in posting this, but now feel glad that I could contribute in some way.
    Think nothing of it, we strive to create an enviroment where all are welcome to, and encouraged to, post their hypotheses. If there is something wrong, we will point it out, but that is never an attack on your intelligence or person, simply us contributing to refine the work you set out to create.

    Please feel free to continue to post anything you find relevent in the future

  6. #6
    "The last assumption comes in regard to the time period over which Doricís line had time to proliferate. Assuming that the starting point came approximately around the Exodus (0 A.E.), I then established that the overall time period for which Doricís offspring could multiply was 1,070 years, the time between the Exodus and the start of the game. So using the model I had established, the equation written out appeared like this...."

    I think Doric was around long before 0AE:

    Monument text of historical marker at King's Watch:

    Founded: Season of the Phoenix, 1 A.E.
    To endure is greater than to dare;
    To keep heart when all have lost it;
    To forego even one's own life when the end is gained;
    Who can say this is not greatness?

    On this site, more than one hundred years prior, the first king of the new Republic of Ascalon was crowned. It was dedicated on this, the ninety-fifth day of the year, in the Season of the Phoenix, in honour of the passing of the greatest of all kings. The stone stands in memory to the first of all sons of Ascalon, King Doric. For it is through his sacrifice that we now live on. May his blood have been spilled for the good of all.

    Would 100 years +- (possibly more) change your numbers significantly? Also, he would not have been crowned at birth thus my "hypothesis," such as it is, that he was one of the first if not the first human on Tyria.

  7. #7
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    Quote Originally Posted by Warison
    "The last assumption comes in regard to the time period over which Doricís line had time to proliferate. Assuming that the starting point came approximately around the Exodus (0 A.E.), I then established that the overall time period for which Doricís offspring could multiply was 1,070 years, the time between the Exodus and the start of the game. So using the model I had established, the equation written out appeared like this...."

    I think Doric was around long before 0AE:

    Monument text of historical marker at King's Watch:

    Founded: Season of the Phoenix, 1 A.E.
    To endure is greater than to dare;
    To keep heart when all have lost it;
    To forego even one's own life when the end is gained;
    Who can say this is not greatness?

    On this site, more than one hundred years prior, the first king of the new Republic of Ascalon was crowned. It was dedicated on this, the ninety-fifth day of the year, in the Season of the Phoenix, in honour of the passing of the greatest of all kings. The stone stands in memory to the first of all sons of Ascalon, King Doric. For it is through his sacrifice that we now live on. May his blood have been spilled for the good of all.

    Would 100 years +- (possibly more) change your numbers significantly? Also, he would not have been crowned at birth thus my "hypothesis," such as it is, that he was one of the first if not the first human on Tyria.
    You are most certainly correct Warison. Remember, King Doric had an audience with the Old Gods in Orr. That means they were still around when he went there. So he undoubtably was around before they left.

  8. #8
    Oops, I forgot about the King's Watch monument. I used the timeline off of guildwars.com and it didn't make too clear on when Doric met with the gods. Since Doric was the first king of Ascalon, I probably should have used the founding of Ascalon as the starting point. But you never know, Rome predated its emperors, and the US survived almost ten years before George Washington was president. Anyway, I punched in the new numbers and the results are:

    62,264 male descendants, which based on my 1:1 ratio makes for

    124,527 total descendants of King Doric.

    If I further extend the equation to population (20 regular people for every one chosen) that gives us a human population of Tyria at 2,490,543 total. Congrats GW players! A few of you have been certified as Chosen again. (But, boy, now I'm wondering if the Charr were some sort of game warden race: Thinning out the numbers of humans so that we don't overpopulate the place ). Thanks for your input.

  9. #9
    Took differential equations?

    Ah...the Malthusian growth curve...well done and calculated. Now could ye use us the logistic growth curve, with "b" the birth rate, "d" the death rate, "a" the...er...garrr, forgot. But, if ye remember the logistic growth curve, ye could try and calculate the carrying capacity of Tyria.

  10. #10
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    Wait, I just thought of something. Did you factor in deaths to you equation? Also, there were several wars in between Dorian times and now, so that would cause deaths, and we also have the Mursaat and the Bloodstone issue...

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