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 Post Posted: Fri Jan 24, 2014 11:48 pm 
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This has been bugging me for a long time, but the issue has been raised again and I've finally decided that it's probably worth creating a thread, just to see if anyone has any possible explanations for it. I'm talking about this from Book 0, Episode 1:
"This thread was being drawn up by the system of the world. Thinkamancers knew it as a 'Grandiocosmic string.' Its numbers were being shaped and guided by the firmament, by what magic theorists called the Erf Axis."

Is this really saying that the Erf Axis is the firmament? Does that mean that "Erfworld" is a bit like saying "sky-world"? Erf sounds like earth, so I always associated it with the ground, but in retrospect assuming that two words are connected just because they sound similar seems foolish. But why the firmament of all things? And why call it Erf? Is there some reference that I am missing? Has anything ever been revealed about where the name Erfworld comes from?

In Lord Crush - Part 5 thread, Lipkin wrote:
Firmament means "vault of heaven" or "sky." In this context, it clearly means the former.
If that's clear, then I'd appreciate someone explaining why. As far as I can tell, "vault of heaven" is just a flowery way of saying "sky", so why it should be one rather than the other is a mystery to me.

As I understand the firmament, it is a mythical dome that covers the world and supports things that people see in the sky. When rain falls it is leaking through the firmament and stars are lights attached to the firmament. Surely we shouldn't take it literally and conclude that Erfworld actually has a real physical dome like that. I think this is the only place that the firmament is ever mentioned, but then again it seems to be a rare glimpse into the underlying nature of Erfworld, so it might be our only hint at a deep truth.

Even more crazy than a dome over Erfworld, maybe the firmament of Episode 1 is actually the one and only firmament, the same firmament that myth says is over Stupidworld. If Erf actually means that firmament, then Erfworld ought to be the world that sits on top of the firmament, so Erfworld's ground is Stupidworld's sky. That would explain why they use a word that sounds like "earth" to say "firmament", but it just can't be what was meant.

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     Post Posted: Sat Jan 25, 2014 12:27 am 
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    Reading the text again, I don't think the firmament is the erf axis. I think the firmament was using the erf axis to guide and shape the numbers. If the "by" were removed, it would be describing the firmament as Erf axis.

    Also, it appears I had an incomplete understanding as to what "vault of heaven" meant. I thought it was literally talking about heaven, and so I was suggesting that firmament was being used as a metaphor for beyond the vale. I was wrong.

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     Post Posted: Sun Jan 26, 2014 5:07 pm 
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    Lipkin wrote:
    Reading the text again, I don't think the firmament is the erf axis. I think the firmament was using the erf axis to guide and shape the numbers.
    That only shifts the mystery slightly. It still means that the firmament and the Erf Axis are closely connected, since the Erf Axis is the magic that the firmament uses to shape the numbers. That still suggests that "erf" might mean firmament.

    The world "erf" actually has dictionary definitions. According to wiktionary, an erf is an inheritance. Is that just an obscure word that happens to be spelled the same as the erf of Erfworld, or is that actually a meaningful connection?

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     Post Posted: Sun Jan 26, 2014 6:30 pm 
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    Lilwik wrote:
    That still suggests that "erf" might mean firmament.


    Only if shaping the numbers using the Erf axis is all that the firmament does. I think it probably does much more.

    Lilwik wrote:
    The world "erf" actually has dictionary definitions. According to wiktionary, an erf is an inheritance. Is that just an obscure word that happens to be spelled the same as the erf of Erfworld, or is that actually a meaningful connection?

    Probably a coincidence, but I wouldn't be surprised if it came up later.

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     Post Posted: Sun Jan 26, 2014 7:04 pm 
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    I think I've seen firmament used in fantasy settings to mean what would be called aether in Victorian science, which is where my interpretation came from. But in all honesty I can't remember any examples off hand.

    Aether
    Ectoplasm

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     Post Posted: Wed Jan 29, 2014 12:22 pm 
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    My best guess is that Erf-Axis is something abstract and intangible. The use of the word "firmament" is merely describing the nature of the Erf-Axis. It's intangibility, yet ever-presence. The spirit of Erf is "like the wind, which blows where it wants to. You hear it's sound, but you can't tell where it comes from or where it's going".

    Due to the reference-based nature of Erfworld, I feel compelled to point out the most famous use of Firmament.

    Genesis 1: http://www.biblegateway.com/passage/?se ... rsion=NKJV
    Quote:
    Then God said, “Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.” 7 Thus God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament; and it was so. 8 And God called the firmament Heaven. So the evening and the morning were the second day.
    ...14 Then God said, “Let there be lights in the firmament of the heavens to divide the day from the night; and let them be for signs and seasons, and for days and years; 15 and let them be for lights in the firmament of the heavens to give light on the earth”; and it was so. 16 Then God made two great lights: the greater light to rule the day, and the lesser light to rule the night. He made the stars also. 17 God set them in the firmament of the heavens to give light on the earth, 18 and to rule over the day and over the night, and to divide the light from the darkness. And God saw that it was good. 19 So the evening and the morning were the fourth day.

    20 Then God said, “Let the waters abound with an abundance of living creatures, and let birds fly above the earth across the face of the firmament of the heavens.”


    Rob may or may not be making a connection here, but if we're talking about the creation of a world, I'd assume there is high chance.

    I don't have a clue how that would tie in except that here is seems synonymous with "Sky", but is also equated with the term "Heaven".
    It is also to note that in Jewish mythos, there are 3 heavens: The Sky, Outer Space, and God's abode. http://www.pastoredcollins.org/archives ... eavens.jpg

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     Post Posted: Wed Jan 29, 2014 12:45 pm 
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    What if it's a giant metaphor for the game table?

    Read through Episode 001, equating Erf-Axis = the Rulebook, and Fate-Axis = The Players and/or GM, and Numbers-Axis = Dice rolls/Modifiers derived from the Rulebook.

    It's imperfect, but, here it goes:
    One day, the GM had no concept of Roleplaying (country of zero). But then the zeroes became 1s, 5s, 48s, Agitated 100.12s, Angry 63.79s, as the first rulebook was bought, it became addictive and he spent more and more money on it.
    Monetary investment soon was exponentially overshadowed by time and energy investment. This thread (progression of addiction) was drawn by the rulebooks. And the rulebooks were responsible for the numbers used in the world.
    But finally, a PC is born into the world as the game begins. And a single PC in the world would be far worth what the GM/Player invested in it.
    But as we all know, a PC is a very dynamic character in the world and will do extraordinary things. Death calls in the game, both to the PC, and the NPCs surrounding him.

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     Post Posted: Wed Jan 29, 2014 3:36 pm 
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    Falcon X wrote:
    What if it's a giant metaphor for the game table?
    How does the firmament fit into that metaphor? Game tables don't seem to have a firmament.

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     Post Posted: Wed Jan 29, 2014 7:11 pm 
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    In Falcon's example, everything not on the game table would be the firmament.

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     Post Posted: Thu Jan 30, 2014 12:31 am 
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    Falcon I think that your analogy is close. Except for the description of Luckamancy dice rolls happen in the Erf Axis. Which makes

    Erf Axis = The game world, the exact locations and stats on all the units and terrain etc. Internal dice rolls happens in units to represent basic decisions, and the terrain and others parts of erf have dice rolls to represent random effects.

    Numbers Axis = Represents the rule book. It takes the contents of the dice rolls, and determines the output.

    Fate Axis = the Game master, the players, and perhaps other forces that effect the functioning of erfworld.

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     Post Posted: Thu Jan 30, 2014 2:42 am 
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    Lilwik wrote:
    Falcon X wrote:
    What if it's a giant metaphor for the game table?
    How does the firmament fit into that metaphor? Game tables don't seem to have a firmament.


    Yeah, sorry, I deviated topic a bit. Let me toss in a few straight-forward ideas:
    A. Grammatically, it would be most correct that "by the firmament" and "by what magic theorists called the Erf Axis" are restatements of each other. Therefore, the Erf Axis is a type of firmament.
    - Perhaps, just as there are X, Y, and Z axises (Length, Width, and Depth) in our world, the three axises of Numbers, Fate, and Erf co-exist in a similar manner on Erfworld. Thus, something could be measured as 3 points down the Erf axis, 5 down the Numbers axis, and 100 down the Fate.
    - If there is an equation for every piece of matter on the grid, a person's g-string might follow a particular pattern. For example, an parabola. A person's Number might breach the Numbers axis at points -8 and +8, thus providing balance, while hitting the Erf and Fate axises somewhere else.

    Conclusion on A: If Erf, Numbers, and Fate are treated visually as axises, in the same way as Length, Width, and Depth, then we are creating a SINGLE SPHERE of mystical, and somewhat tangible space. That fits the understood definition of firmament.
    Thus, it would be implied that a unit's g-string follows a path through the firmament, likely something like an ellipsis or parabola, and that the Erf-Axis is the "smart one" that moves the string to it's proper place in the firmament.

    B. To return it to my metaphor of the game table: As Lipkin implies, firmament is everything not on the game table. It is the intangible space in which rules, ideas, die rolls, and other things collide.
    - Further, if Erf-Axis is the part of the firmament that shapes and guides the g-strings upon unit creation, then perhaps it is actually the one that is symbolically the players or GM, leaving Numbers for the rulebook, and Fate for the Dice.

    Pictures of firmament:
    Spoiler: show
    The Firmament as a whole: http://people.sc.fsu.edu/~jburkardt/m_s ... f1_xyz.png
    A better visual of the firmament: http://ej.iop.org/images/0957-0233/21/4 ... 8fig05.jpg
    What a Unit's g-string looks like, with x=Numbers, y=Fate, and Erf not being shown due to unshown z-axis. http://www.nabla.hr/TranslQuadr.gif

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     Post Posted: Wed Mar 12, 2014 3:42 pm 
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    found myself running around the forums for the first time in forever and saw this. I always assumed Erf stood for the Error Function in math "Erf" is what it's called. And the concept of it fits neatly in to everything erfworld. http://mathworld.wolfram.com/Erf.html and taken from http://en.wikipedia.org/wiki/Error_function

    "The error function is used in measurement theory (using probability and statistics), and although its use in other branches of mathematics has nothing to do with the characterization of measurement errors, the name has stuck."

    To that end the idea that one of the axises of the magics has to do with uncertainty in measurement for probability and statistics I think fits neatly into everything there is about erfworld.

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     Post Posted: Wed Mar 12, 2014 7:46 pm 
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    My theory is the firmament is the sky at the top of the hex, and it rains in rain hexes because the roof is leaky.

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     Post Posted: Wed Mar 12, 2014 9:05 pm 
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    j_scheibel wrote:
    To that end the idea that one of the axises of the magics has to do with uncertainty in measurement for probability and statistics I think fits neatly into everything there is about erfworld.
    I'm curious to see that explained in more detail.

    After thinking about this for a while, I guess we have no choice but to conclude that Erfworld has a firmament. Book 0 explicitly says so, and who are we to assume that is a metaphor? Therefore we know the shape of Erfworld: it is flat and finite with a dome sky. When you get to the edge, you find a wall so high that it actually touches the sky.

    Thanks to Digdoug we can also guess the approximate size of the dome. We know there are hundreds, not thousands of sides. From B0E66 we know that each side has between 1 and 20 capital sites, which means that Erfworld has hundreds or thousands of capital sites, not millions. All we need is a rough guess at how many non-capital-site hexes there are for each capital site and we'd have a rough guess at the size of the dome.

    I'm going to guess that on average each capital site is surrounded by a circle with a radius of hundreds of hexes, not thousands, since we know that 50 move is considered fast in Erfworld and it only took Lord Crush 6 turns to get to Squashcourt territory. So I guess that in total Erfworld has tens of millions of hexes, not billions. Therefore the firmament is a solid dome thousands of hexes in diameter onto which the sky is projected.

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     Post Posted: Wed Mar 12, 2014 9:13 pm 
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    I'm not quite sure how you read that post you linked, but my read is that average number of capital sites per side is probably below 2.

    Lilwik wrote:
    j_scheibel wrote:
    To that end the idea that one of the axises of the magics has to do with uncertainty in measurement for probability and statistics I think fits neatly into everything there is about erfworld.
    I'm curious to see that explained in more detail.

    After thinking about this for a while, I guess we have no choice but to conclude that Erfworld has a firmament. Book 0 explicitly says so, and who are we to assume that is a metaphor? Therefore we know the shape of Erfworld: it is flat and finite with a dome sky. When you get to the edge, you find a wall so high that it actually touches the sky.

    Thanks to Digdoug we can also guess the approximate size of the dome. We know there are hundreds, not thousands of sides. From B0E66 we know that each side has between 1 and 20 capital sites, which means that Erfworld has hundreds or thousands of capital sites, not millions. All we need is a rough guess at how many non-capital-site hexes there are for each capital site and we'd have a rough guess at the size of the dome.

    I'm going to guess that on average each capital site is surrounded by a circle with a radius of hundreds of hexes, not thousands, since we know that 50 move is considered fast in Erfworld and it only took Lord Crush 6 turns to get to Squashcourt territory. So I guess that in total Erfworld has tens of millions of hexes, not billions. Therefore the firmament is a solid dome thousands of hexes in diameter onto which the sky is projected.

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     Post Posted: Wed Mar 12, 2014 10:30 pm 
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    He meant "City Hexes" and was just misspeaking I think.

    Also no acknowledgment of my leaky sky theory. Could this be evidence of an academic conspiracy to suppress a rival theory? I have no doubt.

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     Post Posted: Wed Mar 12, 2014 10:59 pm 
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    Shai_hulud wrote:
    He meant "City Hexes" and was just misspeaking I think.
    No, I'm just allowing for a large margin of error. When making rough estimates it's not a good idea to try to be more precise than you can be sure of. We know at least one side had 15 capital sites at one point, so just to be safe I'm rounding that up to 20 and assuming there might be other huge sides like Haffaton; that way I can be pretty confident that I've got a good upper bound on the average number of capital sites per side. I don't know any way of estimating the number of city hexes per side.

    Shai_hulud wrote:
    Also no acknowledgment of my leaky sky theory. Could this be evidence of an academic conspiracy to suppress a rival theory?
    That's what I mean by firmament. According to Wikipedia, that's the traditional understanding of how rain works under a firmament.

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     Post Posted: Thu Mar 13, 2014 1:29 am 
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    Mostly I was wandering if you could, like, pierce the heavens with your drill.

    Or maybe the sky could fall, or you could fly up and mine the ceiling of the world for space rock.

    Has anybody said "For the World Is Hollow and I Have Touched the Sky" at some point?

    Are those giant red lines in the MK cracks in the heavens? And if so, why is it creepy red instead of raining?

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     Post Posted: Thu Mar 13, 2014 4:09 am 
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    Lilwik wrote:
    No, I'm just allowing for a large margin of error. When making rough estimates it's not a good idea to try to be more precise than you can be sure of. We know at least one side had 15 capital sites at one point, so just to be safe I'm rounding that up to 20 and assuming there might be other huge sides like Haffaton; that way I can be pretty confident that I've got a good upper bound on the average number of capital sites per side. I don't know any way of estimating the number of city hexes per side.


    It should be pointed out that at the time, at least, Haffaton was specifically named the largest side in Erfworld. And, Jillian (a warlord that was well traveled in her profession of hiring out as a merc) hadn't even heard of another side with more than 5 capital sites. And, a successful site would be more likely to average 2-3 capital sites. So, even if there is somewhere another side as big or slightly bigger than Haffaton, odds are there's only one other like that among the few hundred sides out there...and outliers like that shouldn't affect the average that much. Most likely, based on just those two pages, you'd be looking at about 500-600 capital sites. If there were more than a thousand capital sites in Erfworld, I'd be shocked to hear it.

    Also, a radius of 100s (plural) of hexes seems...high. Admittedly, distances like that seem rather fluid in Erfworld, but the distance between the cities of Haffaton and Goodminton (as measured by Jillians escape) was three turns of her walking and 8 turns of flying (with 31 move). And, the story made a point of saying she didn't go straight at all. It doesn't say Jillian's move anywhere I've found, but it seems to me that she probably didn't go far enough in those three Turns to make up for the zigs and zags of dodging scouts and such during those 8 Turns. So, it seems about 240 hexes between the two at most. Even assuming the two capitals are adjacent capitals rather than having a capital Jillian passed by on the way, that suggests about 100-120 hex radius of control around each capital in which there isn't another side. Assuming that distance is typical, that should give an estimated area of 31k-45k hexes per capital site. Assuming Erfworld has its capital sites distributed roughly evenly, and that there are no significant gaps where capital sites' areas can't be counted (like a theoretical ocean or impassible mountain range that divides entire regions of Erfworld) the total area of Erfworld would then range from as low as 15.71 million hexes to as high as 27.14 million hexes. Or, a radius of about 2200-2900 hexes. Very very roughly...and probably running a tad high when not counting those oceans and such...or Magic Kingdom.

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     Post Posted: Thu Mar 13, 2014 12:07 pm 
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    Lilwik wrote:
    j_scheibel wrote:
    To that end the idea that one of the axises of the magics has to do with uncertainty in measurement for probability and statistics I think fits neatly into everything there is about erfworld.
    I'm curious to see that explained in more detail.


    Well, consider this http://www.erfworld.com/wiki/index.php/Magic

    Fate magic is strictly speaking magic that deals with how things "are/should be". if it exists as a tangible real thing this modifies or has access to it. things that work in a Classical mechanics sort of way.

    Numbers magic is all about how things might be. think of it as a game of statistics. If a number is involved it can be manipulated. This deals in averages and randomness. things that work in a quantum physics sort of way.

    Erf magic is all about the manipulation of the two. Think fractals and where you stop in zooming in. Think expression of error on the error's maximum or the error's minimum without actually changing the underlining odds or what things are.

    Calling erf magic the firmament seems poetic. but if I were to pull out some meaning beyond what I said about I'd say.... if firmament is to erf. I see that the heavens don't change math and nature of things but still have influence in the area of error. changing outcomes without changing what things really are or the math behind them.

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