Talk:Christmas tree hat

So its limited edition, and tradeable... So basicaly its a new tradable rare... I thought this wasnt going to happen anymore... 17:12, December 19, 2012 (UTC)
 * It's harder to get than fish mask, and stays here for much shorter, at least 17:14, December 19, 2012 (UTC)


 * Only going to make it more valuable when they take it away.DiabolusMiles (talk) 03:40, December 20, 2012 (UTC)

Well, they did add the Fish mask and we all know how that ended up.Emoted Wolf (talk) 19:33, December 20, 2012 (UTC)

They only said they wouldn't drop free rares all over the place. This one can technically only be bouhgt with real-world money (ie SoF) or obtained through hours of playing (Took me 10 saved-up spins just to get the green present, still haven't gotten any others after 30 min of Runespan, so they're kind of rareish)

I hope to get one to save and at least one more to sell, although I have to decide...is it better for my OCD brain to get this and the mistletoe so I have everything, or save up for two of these...

N1ghtshade3 (talk) 00:44, December 21, 2012 (UTC)

Does any1 have enough gp in game to buy 2 and test this 50m hi alch, 100m low alch that it says on the wiki page, or is it known already some1 trolled the page?Good i snipr (talk) 03:35, December 21, 2012 (UTC)

Where/when did Jagex said they'd be completely removed on the 14th of January? 94.145.226.59 10:23, December 22, 2012 (UTC)


 * Its saying that the presents would be removed not the christmas tree hat. Bluest (talk) 21:35, December 22, 2012 (UTC)

Factual correction
"The Grand Exchange Price has risen exponentially  [dramatically] every day it is updated since its release."

After fixing this, I noticed the change was reverted. Here is a little math lesson:

The price on March 26 was 23,296,136

The price on March 27 was 24,365,128

That is a rise in price of 1,068,992

If the price rose EXPONENTIALLY  the next time it was updated, the market price of the Christmas Tree Hat on March 29th would be 1,142,768,261,192 (over 1 trillion gold), as exponentially would mean 1,068,992 x 1,068,992 = the new 1-day change.

Not only this, but immediately below this trivia entry is "The Christmas Tree Hat doubles in price every 15-16 days that it is updated." which is totally contradictory to the previous trivia entry. If the price rose exponentially, it would more than double (in fact, it would be millions of times higher than it was before) every single day it is updated.

Not once during any period of time since its release has the Christmas Tree Hat ever risen exponentially in price.


 * Exponential functions don't have to be squares. For example, 1,068,9921.0001 is "only" 1070477.0294664 but it's still exponential. Also take note that the word wasn't used here literally; it's a common synonym for rapid growth. Your change is fine, but you shouldn't complain with a misguided understanding. 03:39, March 30, 2013 (UTC)

In that case, any increase or decrease can be considered "exponential". Regardless of whether its misuse has entered the common lexicon as meaning something entirely different, a less ambiguous term is more appropriate. In an encyclopedic entry, things should be described literally. I very seriously doubt the person was describing an increase using a rational exponent. You shouldn't stretch reasoning to preserve a flawed status quo.


 * If you read the latter of my statement, you'd see I didn't care one way or the other about the change. 18:28, March 30, 2013 (UTC)


 * @unsigned user, if you knew anything about exponents, you'd realize that doubling every 15 days would mean it fits one of the most basic exponential graphs, 2^x (where x is the number of 15 day periods).  So in terms of months, that would be increasing at 4^x.  Nice try pretending to know math though.
 * If you just use Google you can see what some exponential graphs looks like Exponential curve
 * Now look at this curve. http://runescape.wikia.com/wiki/Exchange:Christmas_tree_hat   It's either exponential or geometric.  I guess you could just plug in the values and see which curve it fits better using a graphing calculator...
 * Also, time doesn't have to be in 1 day units man.  For something like this, you'd want to use some bigger chunks of time since this is basically like stocks and flucuates frequently for small intervals of time.98.237.74.88 20:00, April 6, 2013 (UTC)

In reply to "if you knew anything about exponents, you'd realize that doubling every 15 days would mean it fits one of the most basic exponential graphs" and "Also, time doesn't have to be in 1 day units man.":

Okay, did you not read the original entry that said "risen exponentially every day"? I'm not arguing that the price couldn't rise exponentially over (X units of time). The edit that I changed said the price has risen exponentially every day it is updated (we're not talking in terms of every 15 days, or in months, the original edit said every day) and that is what I was correcting. Your whole reply only proves my point. Nice job pretending to know what the hell you're talking about... man.


 * It's over, can we just shut up. If you'd like to continue insulting each other about whose answer is right and whose is wrong (which you both are), please find another medium through which to do it. 22:36, April 17, 2013 (UTC)

You're both wrong, but you (most recent editor) more than most. The statement that the price has increased exponentially every day it's been updated, while misleading, is mostly accurate. It doesn't take a rock scientist to see this: plug in the values, and you'll see that the change in price from one day to the next has been fairly constant as a multiple of the previous price, 1.05. In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential. What limited knowledge of exponential functions you appear to have seems to have given you the idea that exponential increases reflect a squaring of the previous value. Not only is this sometimes not the case, as Mol pointed out, it is never the case. Exponentially increasing functions simply rely on the previous value with a multiple greater than 1. That's what's happening here, and that's why the statement is correct.

Now, you might ask why it's exponential. The answer is that the true price has been above the median/guide price since the introduction of the item, and the median price has constantly been revised upwards. Due to limitations set by Jagex, this change can be no more than 5% of the previous value. There's some obfuscating factor where the change starts to be slightly less than 5% over time, but it's still basically accurate to say that the next price will be 5% more than the previous, up until the time that the median catches up with the true price. 22:43, April 17, 2013 (UTC)


 * Multiple: A number that can be divided by another number without a remainder. 1.05 is not an integer and is not a multiple, and the fact that it is a decimal is indicative of a remainder. You are dubiously arguing that any increase at all is exponential, in which case my edit (the price has risen dramatically) stands as less ambiguous, less misleading, and therefore more accurate.
 * You're just laughably wrong. If a p_1 is 5% more than p_0, then the constant of increase, which I validly called a multiple, would be 1.05. What you are arguing is that for an increase to be exponential, the price must be squared every time (????). What I am saying, and what you haven't comprehended, is that if the price increases 5% every updated day, the increase is exponential. Since you managed to figure out what a multiple was through the book Times Tables Done Easy, maybe try looking at a slightly higher level book and figuring out what an exponential actually is. 23:00, April 17, 2013 (UTC)
 * Read over my first post. Where did I say that the price must be squared every time? I used that as an example (i.e. including but not limited to). That said, your argument is based on a false premise.


 * "Exponential increases occur when the growth rate of a mathematical function is proportional to the function's current value."


 * The growth rate fluctuates each day it is updated and is therefore not proportional to the function's value at any given time an increase occurs. There goes you entire argument. In mathematics, "mostly exponential" is not exponential.


 * Your example would never be practical as the price would never be squared under any rational circumstance. Actually, scratch that, it's just completely wrong. And the growth rate is clearly proportional to the current price, with a slight bit of fuzziness due to unknown circumstances -- just as the dragon kiteshield only rose by about 4.7% per day on average, so does the tree hat. The rate of change has fluctuated between 4.5% and 5% every day. It's better to say it's an exponential increase, which for all intents and purposes it is, than to say it's drastically (weasel word) increasing. I think you just made a bad call and either misunderstood the point of the statement or misunderstood the meaning of exponential functions, because your original statement about the increase being 1,142,768,261,192 is so off-base that I can't fathom how you came to that conclusion. The rate of change is proportional to the item's current value. End of story. 23:13, April 17, 2013 (UTC)
 * It is proportional "with a slight bit of fuzziness"? That is not proportional. Any fluctuation in the increase at all means it is not proportional and therefore not exponential. If the increase is proportional on any given day (i.e. it rose in price by 5% on one day) and only rose 4.5% the next, the rise in price is not proportional to the function. Hoever impractical it is, it is mathematics, and when it comes to fuzziness and unknown circumstances, you can say it resembles an exponential increase, you can say that on a graph it looks almost exactly like an exponential increase with an almost impercievable deviation, but it is not truly exponential. End of story, homie.
 * "In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential." Guess who said that 40 minutes ago? This dude! What I can't tell is whether you're suddenly latching on to my admission that the price increase lags slightly below 5% as a cheap way to win an argument, or if you actually meant that from the beginning but you were just singularly bad at articulating the point. In any case "Not once during any period of time since its release has the Christmas Tree Hat ever risen exponentially in price." is clearly incorrect and I hope you realize that. 23:30, April 17, 2013 (UTC)
 * A cheap way to win an argument? Naw. I'd say I am "mostly right" for all intents and purposes, because practically speaking I can't always be right under any rational circumstance. I mean, you could say I was right with with a slight bit of fuzziness due to unknown circumstances.
 * You claimed that the price had never experienced exponential growth, and that to do so the price would have to double. Not true. You claimed that the price could rise exponentially over a period of a month, instead of days. Nonsensical. For most of the item's existence, and to this day if not for Jagex's strange limitations, the price has experienced exponential growth. Nonetheless, a function of (1.04+rand/100)^x would still be considered in the exponential function family even if it not directly proportional to the previous price. In any case, we cannot deal in pure mathematical truths -- it's anal to go after the difference between 4.7% and 5%, just as it's anal to go after rounding errors in the beginning causing the change to be 1.0500006046857966217068379597556 instead of 1.05. I don't really think you have any idea what you're talking about. Sorry. 23:42, April 17, 2013 (UTC)
 * Quote where I said the price would have to double, and don't quote my example as that was just an example of an exponential increase, not the only circumstance.  "In any case we cannot deal in pure mathematical truths."... lol. Then don't use mathematical terms. It's not "anal", it's math, genius. I know you have no idea what you're talking about.
 * Well, exponential growth is also a financial term (no mathematical truths here, pal!) where the price closely resembles an exponential curve. So it's correct, just not in the field you seem to know so much about. I would argue that given that we're dealing with prices and not simply numbers (otherwise they'd be doubles, not integers), this is more accurate. And you said:
 * If the price rose EXPONENTIALLY the next time it was updated, the market price of the Christmas Tree Hat on March 29th would be 1,142,768,261,192 (over 1 trillion gold), as exponentially would mean 1,068,992 x 1,068,992 = the new 1-day change.
 * This implies that you thought exponential increase meant squaring the increase in value, which is not only generally wrong, but always wrong. That is never the case (note that you also said "would", not "could", but onward we go). 23:49, April 17, 2013 (UTC)
 * Onward we go indeed. In my example, it "would", in general it "could". I implied nothing. Trust me, I wrote it. I would know.
 * There is literally no exponential growth equation with integer values where f(x) = (f(x-1)-f(x-2))^2 for ANY value, let alone one relevant to this example. It doesn't work like that. 00:02, April 18, 2013 (UTC)
 * Well, if you add enough fuzziness and unknown circumstances I'd say it resembles an exponential curve, even if it's not one, because after all, there's no point in being precise or anal about it, right?
 * I'm not going to take the ad hominem bait, but you said originally that the price of the hat on the 29th (call it t = 2) would be equal to the difference between the price on the 27th (t = 1) and the 26th (t = 0), squared. That makes absolutely zero sense, can you defend it? 00:10, April 18, 2013 (UTC)
 * Since when is the amount of sense something makes proportionate to its factual accuracy? Do take the bait. I mean, math is subjective. If it resembles an exponential curve to me I can call it one, because there is no point in being anal about it since, you know, this whole article is just an opinion piece. Why get into the pure mathematical details?
 * See, now you're just being a dick. Can you answer the question or were you just horrendously wrong? 00:21, April 18, 2013 (UTC)
 * Nah, I'm being practical.
 * Still waiting for that mathematical defense instead of more snidery. 00:32, April 18, 2013 (UTC)
 * Nah, I don't have to have a mathematical defense. We're discussing similarities and resemblances to mathematical functions, not math.
 * It's funny because you already betrayed your ignorance with your first post, and yet you're trying to act like you know the game. 00:37, April 18, 2013 (UTC)
 * Nah, you asked if I "can" give you an answer, not if I "would", which implies that you don't know the answer or what you're talking about, since implications are a matter of opinion and all.
 * Are you actually getting anything out of this? Last five replies have been stalling and it's getting kind of tiring. 00:45, April 18, 2013 (UTC)
 * Nah, for all intents and purposes they resemble informative pieces of information.
 * Your mathematical skill is matched only by your rhetorical prowess. 00:50, April 18, 2013 (UTC)
 * Except he's not borrowing anything mathematical from what you say. 00:54, April 18, 2013 (UTC)
 * Stahp plz 00:51, April 18, 2013 (UTC)


 * Nah, I'd say my rhetorical prowess resembles that of an expert. Also, my original post was under the assumption that the exponent was an integer, not that the price would necessarily have to double or that the increase must be squared. To have anything other than an integer as the exponent is misleading at best, and although the price is increasing at an increasing rate, when the "fuzziness" is taken into consideration, it is not truly an exponential increase, it is simply an increase.
 * Are you saying that because there are rounding and estimation errors, which there will be in any calculation, it's not a proper exponential? 00:59, April 18, 2013 (UTC)
 * Yes, trolling with my previous statements. Almost Lincolnesque. You still haven't explained that situation though -- increasing an integer exponent by one would not square the value unless the base was 2 and it was the first day, as I said. And as I also said, neither of those circumstances at all fit the situation. So... 01:03, April 18, 2013 (UTC)

No. I am saying that an increase one day of 5% and the next day 4.5% and the next day 6% and the next day 4% is not indicative of a true exponential function. It may resemble an exponential curve, but it isn't one.
 * I don't believe I ever claimed in any part of this that it was a "pure" exponential function such that the increase would be constant (note that this would be impossible, regardless, for any integer prices, so it's a silly point to make a stand on). In my very first post here I noted that the rate was slowing down. You seem to think that exponential curves can only be of that simple, gradeschool form, and that's simply not true. And your original post actually makes less sense now that you've attempted to explain it. What are you even trying to make a point of? 01:08, April 18, 2013 (UTC)
 * If you don't know what I'm trying to make a point of you have no business commenting. I'm trying to explain and you are throwing your preconceived point of view into what I am saying and not actually trying to understand my point. Pure exponential functions are the only exponential functions... otherwise any increase can be considered exponential.
 * I would make a joke here about how useless pure mathematicians are, but you don't seem to have a grasp of the basics yet. 01:14, April 18, 2013 (UTC)
 * I would make a joke about how you should have a firm grasp of pure mathematics before you go making generalizations and abstractions of it.
 * I would make a joke about how none of responses are actually original... They're just reversals of what Cook is saying, slightly twisted to fit your lame argument.
 * http://i.imgur.com/ZC5JHSH.png
 * 01:22, April 18, 2013 (UTC)
 * I assure you that I do, I just don't think it's relevant when we're using adjectives to describe growth trends. On that note I must take my leave -- this stimulating discussion has left me drained. I do hope you think you've won this exchange. In the mean time I have added a note in the trivia section summing up the uniqueness of its price growth -- I hope it fits your high standards. 01:27, April 18, 2013 (UTC)
 * It doesn't.

Don't want to intervene into this conversation, but could the anon please remember to sign your posts with ~ :). Thanks 01:25, April 18, 2013 (UTC)

Your reasoning for calling the increase exponential is about the same argument as saying 3 is not prime because its factors include 2 and 1.5. When people hear "exponential", they assume y in Xy is an integer, because if that isn't the case any increase at all can be considered exponential and the term is meaningless.
 * "When people hear "exponential", they assume y in Xy is an integer"
 * So x^1.5 isn't exponential? Okay.

Apologies, I meant a constant. I was still thinking about the 3 as a prime reference. I was about to edit that but I see you already commented.
 * Delayed reply -- exponentials are of the form c^x, not x^c (where c is a constant). 06:00, April 19, 2013 (UTC)

Blatantly false. That depends entirely on the intended application. A perfect example: You just used a variable (c) to describe a constant. You are clearly educated beyond your intelligence.

See:  http://en.wikipedia.org/wiki/Exponential_function

"The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable."

ex

In any given application (e.g. a Grand Exchange price graph), if the exponent (x) varies it is not a constant change and therefore not an exponential function, however closely it may resemble one. A varying  ( x ) would result in a inconsistent (and therefore not proportional) change.

" In recent days it's tailed off a bit, for some unknown reason, but nonetheless it can still be considered mostly exponential."

That is not exponential growth, that is logistic growth. Exponential functions don't tail off. The fact that it constantly, consistently, and indefinitely increases is the very meaning of exponential. Once you plug in ( x ) it cannot decrease or what you have is not an exponential function because the change is not constant.

See:  http://en.wikipedia.org/wiki/Logistic_function

"The initial stage of growth is approximately exponential ; then, as saturation begins, the growth slows, and at maturity, growth stops."

Approximately exponential is not exponential.

http://img585.imageshack.us/img585/1539/tumblrm7ubi46hiw1rvsnj6.gif

Oh my god, you completely missed the point. You are so wrong that you have to know it at some level. x^c (say, x^2) is not an exponential expression. 2^x is. The whole point of an exponential equation is that the "x" value varies. Let's instead deal with bases and exponents. In polynomial equations, the base is what varies. In your e^x example, the multiplicative rate of change from one x value to the next is e. The fact that we can even take the change from one x value to the next guarantees that the x value varies! In exponential equations, the exponent varies! It's 7th grade stuff, man! And I clearly know what a logistic function is. Take a look at the Christmas tree hat's graph. Is the rate of change slowing down? No? Then it's not logistic! I claimed that the multiplicative rate of change (i.e. the 1.05, or the BASE) was going down slightly. The rate of change of the Christmas tree hat's price has always been increasing. God almighty, you make me laugh and cry at the same time. And try not to incorrectly use logistic functions when you still lack understanding of the difference between a polynomial and a exponential. Jesus. 12:27, April 19, 2013 (UTC)
 * Oh, and you can probably tell I don't like arguing grade school math with imbeciles. 12:30, April 19, 2013 (UTC)

http://img138.imageshack.us/img138/3329/calcy.png

The OP is right. The exponent or the base can be a variable depending on what you're doing. When you're making a price graph, if the exponent varies from day to day it's not an exponential curve. Any increase at all can be exponential the way you're wording it cook.
 * Assuming you're not actually the same guy I've been arguing with for the past few days, x^2 and x^3 are not exponential functions. That's the difference between polynomials and exponentials. If the exponent is based on the number of days gone by, AND THE BASE IS NOT, then it's exponential. The way I'm wording it is that the base varies randomly between 1.04 and 1.05, and the exponent is the independent variable x. No matter how you slice it, that's exponential. 18:11, April 20, 2013 (UTC)
 * In order to clear up some confusion, for a given function $$f(x)$$ to be exponential and not polynomial, there must exist a base (which is allowed to vary) $$a$$, an exponent $$x$$ such that $$x$$ is not constant, and an optional scalar $$c \in \mathbb{R}$$ (for our purposes, c is a real number): $$f(x) = a^{cx}$$. Functions in the form $$f(x) = x^c$$ where $$c \in \mathbb{R}$$, are called polynomial functions. Two of the buttons circled in the picture you linked are such functions. The other may be considered an exponential function with respect to $$y$$. 18:15, April 20, 2013 (UTC)