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Post by legion on Dec 15, 2012 12:02:17 GMT
Well, again: we have proven to a reasonable degree that the comic distribution is *not* random.
What remains to be decided now is if Tom aims for mondays or if he aims for constant chapter length (within a certain substet).
So, if the chapters are always of length x, y or z, what are the odds that the chapters will always end on mondays by accident?
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Post by Corvo on Dec 15, 2012 14:28:56 GMT
...we have proven to a reasonable degree... Hm, sorry, but I think that's the same as saying " we have not proven, but I really, really want it to be true".
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Post by Nnelg on Dec 15, 2012 14:58:45 GMT
Exactly. You're supposed to assume the hypotheses that is opposite to your beliefs is true, then disprove it. Or he could just prove that his hypotheses is true. Well, if he wants to do it using proper statistics, that's the way to do it.
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Post by Corvo on Dec 15, 2012 17:28:30 GMT
Well, if he wants to do it using proper statistics, that's the way to do it. I'm feeling particularly inquisitive today, so can you explain how this proper statistics thing work? I mean, I really want to know it, but I'm too lazy to search for it right now. ;D I just can't see why someone can't simply prove that he is right, instead of proving everyone else is wrong. Is this how science works nowadays? Haha
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Post by GK Sierra on Dec 15, 2012 17:51:20 GMT
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Post by Mezzaphor on Dec 15, 2012 17:57:11 GMT
If you have a thousand points of data consistent with your hypothesis, and one point of data that isn't consistent—and if you can't explain that one point as some kind of experimental error—then your hypothesis is not a completely accurate description of reality. At best it needs to be modified, and at worst it needs to be discarded entirely.
So you can't ever prove a theory. What you can do is demonstrate that your theory fits the data better than any other theory—and simply hope that future data continues to fit your theory, and also hope that some other theory that better fits the data doesn't come along.
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Post by legion on Dec 15, 2012 18:26:06 GMT
...we have proven to a reasonable degree... Hm, sorry, but I think that's the same as saying " we have not proven, but I really, really want it to be true". Well your thought is inaccurate, we have shown that the distribution cannot be random, and so the hypothesis that this is just a coincidence is false; this explicitely leaves us with either Tom is aiming for mondays or Tom is aiming for chapters of constant length.
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Post by Corvo on Dec 15, 2012 18:26:07 GMT
So you can't ever prove a theory. Wow. "Ever", uh? Well, I had this crazy theory that fire is hot, but since I can't ever prove it... Haha, sorry, I just couldn't stop myself. Anyway, I know somethings are harder to prove then others, but if you don't prove it, then it's still just a theory. To be raised to the rank of "true", you have to prove it. That's why scientists continue working to explain the inconsistencies in their theories, instead of lying down and hoping the new data will fit the theory.
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Post by legion on Dec 15, 2012 18:28:37 GMT
No, a theory is true if it fits the data, until it is proven otherwise or a more fitting theory is found.
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Post by Corvo on Dec 15, 2012 18:35:20 GMT
Well your thought is inaccurate, we have shown that the distribution cannot be random, and so the hypothesis that this is just a coincidence is false; this explicitely leaves us with either Tom is aiming for mondays or Tom is aiming for chapter of constant length. Uh? Maybe I lost something, but from what I got, the "prove" that it can't be random is something like " well, it's just very, very unlikely, so I'll assume it's impossible". If it's really that, then it just doesn't work for me. Did I misunderstood?
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Post by Corvo on Dec 15, 2012 18:41:00 GMT
No, a theory is true if it fits the data, until it is proven otherwise or a more fitting theory is found. Well, exactly. If it fits the data. If there's one piece of data that doesn't fit, like Mezzaphor proposed, then you have to explain that before the theory can be considered "true" again.
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Post by Nnelg on Dec 15, 2012 19:35:14 GMT
I just can't see why someone can't simply prove that he is right, instead of proving everyone else is wrong. Is this how science works nowadays? Haha It's how Science has always worked. And it's no trivial matter. It is simply not possible to directly prove a theory. However, it is possible to disprove one. So, the only way to prove one theory is to disprove the alternatives. Well your thought is inaccurate, we have shown that the distribution cannot be random, and so the hypothesis that this is just a coincidence is false; this explicitely leaves us with either Tom is aiming for mondays or Tom is aiming for chapters of constant length. We have shown with a very high degree of certainty ( p << 0.05) that the distribution of comic end days is not a Simple Random Variable. No more, no less. So you can't ever prove a theory. Wow. "Ever", uh? Well, I had this crazy theory that fire is hot, but since I can't ever prove it... Haha, sorry, I just couldn't stop myself. No, that's actually a valid point. Not even that theory can be proven 100%. It can be invalidated with just one counter-example... For instance, Annie's Blinker Stone. Anyway, I know somethings are harder to prove then others, but if you don't prove it, then it's still just a theory. To be raised to the rank of "true", you have to prove it. That's why Science has never produced anything other than a Theory. Even so-called "Laws" can be falsified by future data. (Case in point: Newton's Laws vs. Relativity.) That's why scientists continue working to explain the inconsistencies in their theories, instead of lying down and hoping the new data will fit the theory. That, actually, is a form of bad practice. Strictly following the tenets of the Science Process, one is supposed to reevaluate the old theory from a neutral perspective. Uh? Maybe I lost something, but from what I got, the "prove" that it can't be random is something like " well, it's just very, very unlikely, so I'll assume it's impossible". If it's really that, then it just doesn't work for me. Did I misunderstood? Close enough... "Well, it's just very, very unlikely, so I'll assume that this isn't the case. I could be wrong, but I'm 99% confident that I'm not."Note: Confidence in a statistical analysis is actually a quantifiable term, meaning I could give you a number of exactly how confident I am. Typically, 95% confidence ( p < 0.05) is considered enough to reject the Null Hypothesis (H 0), which is what you're trying to disprove.
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Post by quicksabre on Dec 15, 2012 21:59:40 GMT
Note: Confidence in a statistical analysis is actually a quantifiable term, meaning I could give you a number of exactly how confident I am. Typically, 95% confidence ( p < 0.05) is considered enough to reject the Null Hypothesis (H 0), which is what you're trying to disprove. Great post nnelg. I am really glad that there are people willing to go all science geek here So to bring it back to this example, we rejected the null hypothesis (random chapter end days) with 99.999% confidence (p = 0.0000087). Now there are two competing hypotheses to explain the non-randomness, 1) that the stories are deliberately made to end on Monday, and 2) that the stories are of a length divisible by 3. I think the latter is testable mathematically, but I'm struggling to come up with a solid way to do it. We CAN test whether the frequency of Wednesdays vs Fridays is non-random, which would indicate that we are not looking at random fluctuations from a chapter length that is divisible by 3. And it turns out that the lack of Fridays is significant (p = 0.035), so I am inclined to go for hypothesis 1, although I still wish I would think of a better way to test these.
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Post by Corvo on Dec 16, 2012 1:52:38 GMT
It's how Science has always worked. And it's no trivial matter. It is simply not possible to directly prove a theory. However, it is possible to disprove one. So, the only way to prove one theory is to disprove the alternatives. Hmm, I can't find anywhere that says (let alone explain why) it's not possible to prove a theory, directly or not. Care to post a link? ...with a very high degree of certainty... Tomato, tomato. " It's not proven, but I really want it to be true". And certainty is the absence of doubt. If you have a "degree" of it, then there is doubt and it can't be called "certainty". No, that's actually a valid point. Not even that theory can be proven 100%. It can be invalidated with just one counter-example... For instance, Annie's Blinker Stone. Not sure if you're just joking here, but just in case: No! You found out my weakness! Blinktonites! ;D If not a joke, not worth of an answer, since we're not talking about GC verse. That's why Science has never produced anything other than a Theory. Even so-called "Laws" can be falsified by future data. (Case in point: Newton's Laws vs. Relativity.) Care to post a link to the scientific magazine where you learned that "Science has never produced anything other than a Theory"? ;D That, actually, is a form of bad practice. Strictly following the tenets of the Science Process, one is supposed to reevaluate the old theory from a neutral perspective. Hmm, no, it's not. "Explaining the inconsistences in one's theory" isn't the same as "confirming the theory". Said explanation might very well debunk the theory. So it's more like "finding out why this piece of data didn't fit". Close enough... "Well, it's just very, very unlikely, so I'll assume that this isn't the case. I could be wrong, but I'm 99% confident that I'm not." Well, legion seens to disagree: ...we have shown that the distribution cannot be random, and so the hypothesis that this is just a coincidence is false; this explicitely leaves us with either Tom is aiming for mondays or Tom is aiming for chapters of constant length. And since I was answering his post, I'll stand for my cause. Oh, and it doesn't matter how confident you are, you might still be wrong.
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Post by Nnelg on Dec 16, 2012 3:12:32 GMT
Well, I'm flattered that you think so, and glad that you understand what I'm talking about, but I'm wondering where you got that p-value for lack of Fridays? I'm also trying to consider the fact that Tom may be slowly increasing chapter length, and also that he pads with filler to the next even number. There's a lot of complexity going into this.
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Post by Nnelg on Dec 16, 2012 3:29:32 GMT
Hmm, I can't find anywhere that says (let alone explain why) it's not possible to prove a theory, directly or not. Care to post a link? You answered this one yourself: Oh, and it doesn't matter how confident you are, you might still be wrong. Tomato, tomato. " It's not proven, but I really want it to be true". And certainty is the absence of doubt. If you have a "degree" of it, then there is doubt and it can't be called "certainty". Incorrect. In Statistics, "Certainty" is a definite, quantifiable term representing how well the data matches one's conclusions. Not sure if you're just joking here, but just in case: No! You found out my weakness! Blinktonites! ;D If not a joke, not worth of an answer, since we're not talking about GC verse. I do not consider this a joking matter. And it is irrelevant what universe we're talking about, the point is still the same: I was demonstrating how even a theory as simple as "Fire is hot" can be disproven by a single counter-example. Care to post a link to the scientific magazine where you learned that "Science has never produced anything other than a Theory"? ;D Care to enlighten me about something it has produced that is not? Hmm, no, it's not. "Explaining the inconsistences in one's theory" isn't the same as "confirming the theory". Said explanation might very well debunk the theory. So it's more like "finding out why this piece of data didn't fit". That's still prejudiced, favoring explanations which are in line with current theories over ones which are not. Strictly speaking, best practice would be to throw out everything and start over. Well, legion seens to disagree: ...we have shown that the distribution cannot be random, and so the hypothesis that this is just a coincidence is false; this explicitely leaves us with either Tom is aiming for mondays or Tom is aiming for chapters of constant length. I'm afraid I'll have to say he is wrong, then.
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Post by Corvo on Dec 16, 2012 5:19:44 GMT
Oh god, this is going nowhere. Well, lets go back for a while and make things clear. My whole point here is: This Monday thing can be just a coincidence. Period. I'm not even saying it is impossible. Just that it can be a coincidence. All the rest is just me trying to have a conversation. I realise I may look a bit agressive sometimes, but it's mostly because (1) my english isn't very good (see signature) and (2) that's how I usually talk with my friends, with sarcasm and jokes and laughing all the time at each other's faces. So with this I'm stating that I'm not trying to start a war here, man. Relax. Now lets finish this... You answered this one yourself: Now if I just had my PhD in SCIENCE! ;D Really, when I asked for a link, I was being serious. I'm not doubting the "theories can't be directly proven" thing, I just can't find the logic of it. So, please, can you give a link or any other reference to somewhere where I can learn more about it? Incorrect. In Statistics, "Certainty" is a definite, quantifiable term representing how well the data matches one's conclusions. Oh, I didn't know you were using this "statistical term" thing. But that only proves that your grammar was correct. A "high degree of certainty" still isn't "absolute certainty". I do not consider this a joking matter. I'm sad to hear this. The world could use a little more sense of humor. And it is irrelevant what universe we're talking about, the point is still the same: I was demonstrating how even a theory as simple as "Fire is hot" can be disproven by a single counter-example. Well you shot right at the wrong direction, then. I never doubted something "can be disproven by a single counter-example". My point with the "fire is hot" thing is that you can prove that the fire is hot. Care to enlighten me about something it has produced that is not? The Burden of Proof Fallacy? Really? Well, sorry, but you made the claim that "science has never produced anything other than a theory". I'm curious to hear where you learned that. Please, tell me. ;D That's still prejudiced, favoring explanations which are in line with current theories over ones which are not. Strictly speaking, best practice would be to throw out everything and start over. "Finding out why the data didn't fit with the theory" is "favoring explanations"? You'd throw out all your research after finding a single inconsistence, without analising why it happened in the first place?! Well, please stay away from my researches, haha. I'm afraid I'll have to say he is wrong, then. That's EXACTLY what I thought! Wow, we have so much in common! Hey, let's grab a beer together someday! ;D
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Post by Mezzaphor on Dec 16, 2012 6:39:36 GMT
Well you shot right at the wrong direction, then. I never doubted something "can be disproven by a single counter-example". My point with the "fire is hot" thing is that you can prove that the fire is hot. "Any theory can be disproven by one contradictory data point" is precisely by nothing can be definitively proven. Saying that something is definitively proven implies knowledge of the future (and sometimes the past) that we just don't have. If you stick your hand in a fire, you aren't proving that all fire is hot. You're just proving that specific fire is hot at that specific moment. However, after sticking our hand in a fire for the five hundredth time and noting that, yep, that fire is also hot, we conclude that "Fire is hot" is a very well-supported hypothesis, so we can probably better spend our time testing other hypotheses. A layman, speaking in an informal, non-scientific context might then say that it's been proven that "Fire is hot". Later, the scientist and the layman both encounter Annie's cold blinker stone fire. The layman, who took "Fire is hot" as a proven, immutable fact, flips a table and screams "Everything I know is a lie!" The scientist just says, "Well, I guess we need to tweak that 'Fire is hot' hypothesis."
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Post by legion on Dec 16, 2012 12:15:23 GMT
In the interest of this thread not lasting 30 pages, I'd like to remind everyone involved that being skeptical is not the same thing as being hypercritical. The former is what scientists do. The latter is what conspiracy theorists do [and holocaust deniers, but let's not mention them ... aw damn].
Both statitiscal analysis and common sense point toward the idea that yes, Tom is actively curtailling his chapter so that they always end on monday or have their length be a multiple of three. We have provided evidence against the null hypothesis. Unless you can show that this evidence is not solid, this discussion has no purpose anymore.
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Post by quicksabre on Dec 16, 2012 14:36:39 GMT
Oh god, this is going nowhere. Well, lets go back for a while and make things clear. My whole point here is: This Monday thing can be just a coincidence. Period. I'm not even saying it is impossible. Just that it can be a coincidence. Hey, that's what I'm saying too! Except as nnelg is saying, I have QUANTIFIED the chance of it being a coincidence. And that chance is roughly 1/115,000.
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Post by quicksabre on Dec 16, 2012 14:44:12 GMT
Well, I'm flattered that you think so, and glad that you understand what I'm talking about, but I'm wondering where you got that p-value for lack of Fridays? I'm also trying to consider the fact that Tom may be slowly increasing chapter length, and also that he pads with filler to the next even number. There's a lot of complexity going into this. I used the same method as for the mondays, except I assumed 22 mondays as a given. So there are 8 remaining days with a 50% chance of being either Wednesday or Friday. I use the R statistics package, it is open source so you can check it out if you want. This was my code: > pbinom(1,8,.5) [1] 0.03515625
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Post by GK Sierra on Dec 16, 2012 20:47:25 GMT
Tom: "Uh-oh, these guys have discovered my secret plot to only start and end chapters on a certain day, FUCK! Now my only secret plots left are putting the staples in the rubber band drawer and sugaring my tea with one cube instead of two!" I'm also trying to consider the fact that Tom may be slowly increasing chapter length, and also that he pads with filler to the next even number. There's a lot of complexity going into this. Filler, huh? I don't know about you, but if I thought a webcomic I was reading was padding, I wouldn't read it. Luckily I can't point to any page and say "this is filler", because I don't believe there are any. I do not consider this a joking matter. Then may I humbly suggest short break to cool off? It's a webcomic, not the general theory of relativity. There is speculation, and then there is pedantry, and I believe this has strayed into the latter.
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Post by Nnelg on Dec 16, 2012 20:57:57 GMT
Well, I'm flattered that you think so, and glad that you understand what I'm talking about, but I'm wondering where you got that p-value for lack of Fridays? I'm also trying to consider the fact that Tom may be slowly increasing chapter length, and also that he pads with filler to the next even number. There's a lot of complexity going into this. I used the same method as for the mondays, except I assumed 22 mondays as a given. So there are 8 remaining days with a 50% chance of being either Wednesday or Friday. I use the R statistics package, it is open source so you can check it out if you want. This was my code: > pbinom(1,8,.5) [1] 0.03515625 Ah, I see. Well, you're assuming the day the end date changes to is random, as well. But consider this: let's ignore for a minute all other factors, (like filler) and assume Tom is steadily increasing the length of comics by 1 page per comic. Now, suppose that some arbitrary comic has a length that is a multiple of three, and ends on a Monday. The next comic, being exactly 1 greater than a multiple of three, would always end on a Wednesday. Now, the comic after that, being 2 greater than a multiple of three, would end two (posting) days after Wednesday, wrapping around to Monday. Then the one after that, being exactly a multiple of three, would also be a Monday. And so, the pattern would be "MWMMWMMWM". Which is pretty darn close to what we actually see. I'm going to go make a list for chapter lengths, and see if there's a more discernible pattern there.
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Post by quicksabre on Dec 16, 2012 21:47:49 GMT
I do not consider this a joking matter. Then may I humbly suggest short break to cool off? It's a webcomic, not the general theory of relativity. There is speculation, and then there is pedantry, and I believe this has strayed into the latter. The thing that is not a laughing matter is not the webcomic, that IS a laughing matter, and for my part I enjoy applying science to random problems. I think it is hilarious that people (including me) are willing to do this, and I'm sure nnelg would agree with me. I apologize if you think it is pedantic, I think it is fun, even if it is irrelevant. What nnelg says is not a joking matter is the nature of scientific understanding. It is understandable that it might irk him if someone tries to undermine this with a joke.
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Post by Georgie L on Dec 17, 2012 3:27:15 GMT
The Theory that Jack built by Frederick Winsor, this reminds me of much.
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Post by Nnelg on Dec 17, 2012 3:35:56 GMT
Then may I humbly suggest short break to cool off? It's a webcomic, not the general theory of relativity. There is speculation, and then there is pedantry, and I believe this has strayed into the latter. The thing that is not a laughing matter is not the webcomic, that IS a laughing matter, and for my part I enjoy applying science to random problems. I think it is hilarious that people (including me) are willing to do this, and I'm sure nnelg would agree with me. I apologize if you think it is pedantic, I think it is fun, even if it is irrelevant. What nnelg says is not a joking matter is the nature of scientific understanding. It is understandable that it might irk him if someone tries to undermine this with a joke. That's right. I personally find forming rational arguments over something as trivial as a webcomic vaguely amusing, and (usually) not very frustrating at all. But the principles of Science are not trivial. They are by their very nature a serious matter.
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Post by Nnelg on Dec 17, 2012 3:42:06 GMT
Anyways, I looked up all the chapter lengths, starting with chapter 11: 17 +2 27 +1 29 +1 35 +12 25 +1 29 +1 33 +1 43 +3 31 +1 29 +1 31 +1 23 +12 25 +1 35 +1 29 +2 25 +1 27 +1 25 +1 17 +1 27 +1 43 +12 23 +3 29 +1 47 +1 25 +1 27 +1 23 +1 29 +1 35 +1 35 +1 Man, do I ever wish this forum had a "spoiler" function. (The +# represents strips between the end of one comic and the beginning of the next, such as bonus pages.)
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Post by GK Sierra on Dec 17, 2012 7:05:42 GMT
The thing that is not a laughing matter is not the webcomic, that IS a laughing matter, and for my part I enjoy applying science to random problems. I think it is hilarious that people (including me) are willing to do this, and I'm sure nnelg would agree with me. I apologize if you think it is pedantic, I think it is fun, even if it is irrelevant. What nnelg says is not a joking matter is the nature of scientific understanding. It is understandable that it might irk him if someone tries to undermine this with a joke. That's right. I personally find forming rational arguments over something as trivial as a webcomic vaguely amusing, and (usually) not very frustrating at all. But the principles of Science are not trivial. They are by their very nature a serious matter. No, don't get me wrong, I love science for science's sake, but it almost sounded an argument was breaking out, and that just... boggled my mind for a moment. Man, do I ever wish this forum had a "spoiler" function. I usually use yellow text as my spoiler because it's fucking impossible to read without highlighting, but I think you wanted to make it actually close up like a menu.
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Post by warrl on Dec 22, 2012 5:14:29 GMT
I am not going to do an actual statistical analysis because (a) it has been far too long since I studied or used formal statistics (b) there isn't enough of the data I want to look at to be statistically meaningful.
But I have a couple of comments:
* If Tom is trying to make chapter length a multiple of 3, then it should be relatively unusual that the chapter-end day changes. In other words, if it had been Monday but then a chapter runs a bit long and ends on Wednesday, then chapters should end on Wednesdays for a while - until there is another wrong-length chapter.
* If Tom is trying to make chapters end on Monday, then when a chapter runs a bit long and ends on Wednesday (or Friday) the next chapter should usually end on Monday.
Looking at the data, there are eight occasions (since MWF updates began) when a chapter ended on a day other than Monday. On seven of those occasions, the next chapter ended on Monday.
The evidence is more consistent with the notion that Tom actively tries to end chapters on Monday.
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