"It is no more likely that the tenth marble will be blue than it is that it will be red."
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Voting Style:  Open  Point System:  7 Point  
Started:  2/5/2010  Category:  Science  
Updated:  7 years ago  Status:  Voting Period  
Viewed:  6,436 times  Debate No:  11106 
Debate Rounds (4)
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This is a quote from a packet over Francis Bacon. The full situation is that a man draws nine blue marbles out of a bag of ten. According to the packet, Bacon's contemporaries claimed that the tenth marble is just as likely to be red as it is likely to be blue. I am against this notion.
The man has no idea how he obtained this bag. This scenario allows for speculation, but no speculations may be confirmed within the given scenario. As for definitions, blue and red are two very different colors. The blue marbles are assumed to be a perfectly solid blue, with no traces of red. Marbles are colored, glass spheres. Good luck to whoever accepts this debate. We shall start debating in Round 2.
I accept this debate, and will help restate Francis bacon as such: The mere repetativeness of the occurance of an incident does not guarentee that the same thing will happen again. His example: Suppose a man draws nine blue marbles out of a bag of ten marbles. It's no more likely that the tenth marble will be blue than it is that it will be red. The previous instances do not guarentee anything about the following instance. I wish my opponent luck, and I hope for this to be an interesting debate. 

I would like to thank Vi_Veri for accepting this debate.
Now, to the debate. Contention 1: Red marbles might not exist. We have proof that blue marbles exist. The man already pulled nine of them out of the bag. However, we do not have proof that red marbles exist. Perhaps nobody has red marbles. It is likely that the previous owner of this bag did not have access to red marbles, and only had access to blue glass to make blue marbles out of. With proof of the existence of blue marbles, but no proof of the existence of red marbles, the marble in the bag is more likely blue than red. In any event, the number of blue marbles and red marbles in the world are different. Therefore, an equal chance of pulling either one out of a bag is highly unlikely. Contention 2: Reason favors the blue marble. People often group marbles by color. Here is a commercial bag of only blue marbles, for example: http://www.arcatapet.com... There exist numerous bags of only blue marbles. Therefore, it is quite likely that this bag, like the others, has all blue marbles. However, few bags exist with mostly blue, but few red, marbles. Contention 3: Probability favors the blue marble. If the bag were filled with ten blue marbles, then it is guaranteed that the first nine would be blue. If the bag were filled with nine blue marbles and one red marble, the chance of pulling out nine blue marbles would be 9/10 * 8/9 * 7/8 * 6/7 * 5/6 * 4/5 * 3/4 * 2/3 * 1/2, or 1/10. Therefore, even if you were to assume that there is an equal chance of a given bag having ten blue marbles or nine blue marbles and one red marble, if a red marble existed in the bag, it most likely would have been revealed by now. Contention 4: There are more marbles than just red and blue. If the marble is not blue (unlikely, given that we place blue marbles with other blue marbles and all), then it's still hardly likely that the marble is red. After all, it could be green, yellow, pink with purple polkadots, or even clear. To assume that the marble is equally likely red as it is blue is to also assume that it is equally likely to be any other color. And yet, you still don't even know if those color marbles even exist. (This ties back to Contention 1.) Therefore, the safest assumption one could possibly make about the last marble is that it is blue. With that, I'll leave the debate to my opponent.
Thank you, Mongeese, for this wonderful debate. The best of luck!  I. To begin by introducing the Black Swan problem. This refutes many of my opponent's points: If all of the swans a watcher of these birds has ever observed are white, they might make the conclusion that all swans are white. But of course, this form of induction (which is the exact course my opponent is also taking) and is clearly unfalsifiable. Inductive inferences have the unfortunate problem of making a general claim from a couple of individual cases. This, of course, is a slap in the face to logic. In fact, shockingly to our swan watcher, there are black swans (in Australia), and finding just one of them will falsify this claim. II. My opponent can not make the claim, "In any event, the number of blue marbles and red marbles in the world are different. Therefore, an equal chance of pulling either one out of a bag is highly unlikely," because my opponent can not prove that there are not equal amounts of blue and red marbles in the world. Unbeknownst to him, there may be millions and millions of red marbles in the world, and only 9 blue marbles. III. Also, my opponent can not use bags of blue marbles he finds online as his proof that bags of blue marbles exist while still claiming that I can not prove that red marbles exist. In similar fashion to my opponent, proof of red marbles existence: http://www.photoradar.com... If my opponent wishes to deny this evidence of the existence of red marbles, he must deny his evidence of the existence of bags of solely blue marbles. IV. The repetition of an event does not guarantee that the same thing will happen again. This is quite evident in the real world and even at the base level of all reality (like quantum physics). Reality has so many factors bumping into one another that one can not guarantee anything, but only hope to apply the scientific concept of falsifiability to a problem. Until falsified, the probability of there being a red marble, and the probability of there being a blue marble, are equally likely if one is properly using scientific theory. V. An example of there being one red marble while there being nine blue marbles would be for a type of game (much like billiards has a single unnumbered ball). My opponent can't rule out this suggestion. VI. I do completely agree with my opponent when he says that the last marble could be green, or yellow, or any other color. I believe that it is equally likely that the last marble is red, blue, yellow, green, or multicolored. This doesn't disprove my claim at all. Just because it is equally likely that the last marble may be yellow does not mean that it is not equally likely that it might be red as well! VII. My opponent's probabilities point doesn't disprove my suggestion what so ever. He claims, "Therefore, even if you were to assume that there is an equal chance of a given bag having ten blue marbles or nine blue marbles and one red marble, if a red marble existed in the bag, it most likely would have been revealed by now." But, just because it is "most likely" to have come out by now, it doesn't mean that it doesn't exist. Say you really did have a bag of 9 blue marbles and 1 red. And say, as you pull the marbles out, you, by chance, don't pull out the red marble until the very end. Just because you pulled out the red marble at the end does not mean that it doesn't exist! It's still in the bag, but unfortunately for it, chance just happened to have the person pulling marbles grabbing a blue one until the very end. VIII. My opponent does not know who put the bag of marbles together, what their intentions were, and what marbles they had at hand. It is impossible for my opponent to prove that the maker of the bag of marbles had only blue marbles.  To conclude, my opponent has not successfully refuted that the likeliness of the marble being red (or green, or yellow, or purple for that matter!) is equal to the likeliness of there being a final blue marble in the bag. The problem of induction and the concept of falsifiability are on the side of equal chance. 

I would like to thank Vi_Veri for responding.
I. For the Black Swan problem, if a European were presented with a cage of ten swans, and the first nine that flew were all identical and white, it would be very logical for him to assume that the last one is white. The chance of the last one actually being black is far below 50/50. The generalization does not prove that all swans are white; however, given that most swans seen are white, the chance of a given swan being white is greater than the chance of that swan being black. This fact still seems apparent today, given that there are more white swans than black swans. Let me use another analogy with righthanded people and lefthanded people. Ten people are in a tent. Nine of them walk out. They are all righthanded. What is the dominant hand of the final person? Given that nine out of nine so far are righthanded, righthanded people most likely dominate lefthanded people in the population. So far, you don't even know that lefthanded people exist in this place. As common statistics and the given nine righthanded people would conclude, the final person is most likely righthanded. My opponent would perhaps argue that the last person might be the sole lefthanded person, to represent the 10% of the lefthanded population, assuming that such a population even exists. However, this would be the fallacy of assuming that a sample is a perfect portion of a whole. It would be considerably easy to randomly get ten righthanded people; as opposed to getting the first nine people as righthanded, while the one person staying in the tent is lefthanded. The chance of the former, assuming a 9:1 ratio of righthanded people to lefthanded people, is 0.9^10 (0.34867844); while the chance of the final person being lefthanded is 0.9^9*0.1 (0.038742049). My opponent makes the error of assuming that I argue in terms of the absolute, not of the likely. II. I will concede that we do not know the quantity of marbles in existence; we only know that the bag maker had access to blue marbles. III. My opponent claims that she has proven that red marbles exist. However, in the land that this man is in, red marbles might be unheard of. We have proof that blue marbles exist only because the man has seen blue marbles himself. The bag was not proof of the existence of blue marbles in the man's area, but rather evidence that people often group similarlycolored marbles together. IV. My opponent again switches from a true statement on absolutes to a false statement on probability. The fact that the tenth's marble is not guaranteed to be blue does not mean that the marble is equally likely blue as red. So far, all arguments on DDO originally appear to be in either black or blue/purple font (hyperlinks) on this computer. I theorize that when I post this argument, it will appear black. However, I cannot prove that the argument will appear black. According to my opponent, because I cannot prove that my argument will appear black, it is just as likely to be red, neon green, fuchsia, pink, or invisible as it is likely to be black. Common sense tells me that this is not the case, and that it is almost guaranteed that my argument will appear black. If the color black is supposed to be as rare as the other colors, and the others greatly outnumber the color black, the chance of my argument being black, according to my opponent, is extremely slim. Therefore, I propose an avatar bet to my opponent that on most people's computers, my argument for Round 4 will appear to be the same color as all previous arguments in this debate. Two weeks. If my opponent is so sure that this chance is slim, she will probably accept. Additionally, I cannot prove that my table will not shoot five feet into the air at any given time. Therefore, should I always assume that there is a 50% chance that the table will shoot five feet into the air, avoiding the table altogether? No. This would be the thinking of a madman. VVI. My opponent claims that the tenth marble might be red for a type of game. I agree that I cannot rule out this suggestion. However, I can state that this is less likely than it is that this is just a bag of blue marbles, packaged to be delivered to one person together. Let's give myself horrible odds here, and say that there's only a 30% chance that the marbles were organized by color in the bag, and a 70% chance that the bag is for a game with nine blue marbles and one marble of another color. This other color could still be yellow, green, multicolored, invisible, red, pink, neon green, sky blue, black, white, etc. Going by my opponent's concession that all of these results are equally likely, that leaves only a 7% chance of the final marble being red, and I haven't even listed a tenth of the colors yet! The basic fact that the color red cannot be advanced ahead of the other colors means that it cannot hope to compete with the color blue, the only color of marble that has been witnessed so far. VII. My opponent agrees that if the red marble were in the bag, it would most likely come out of the bag by now. Given that what would be expected of the red marble has not occurred, this cannot help the case of the red marble at all. It has not shown itself nine times out of ten, so there's really not much trust we can put in the red marble that it actually exists. This probability problem does not exist if the final marble is actually blue. VIII. My opponent claims that it is impossible for me to know that the maker of the marble bag only had access to blue marbles. However, I merely need the acknowledgement that there is a chance that the bag maker only had access to blue marbles, which my opponent apparently concedes. If this chance is true, then we know that the final marble cannot be red, although it could still easily be blue. This slight boost in the chance of the final marble being blue clearly puts it ahead of the color red. In conclusion, the fact that the first nine marbles were blue clearly supports the idea that the final marble will be blue. The color blue is an established color of marble, while red must first compete with yellow, green, purple, invisible, orange, and numerous others for being the unmentioned color. Vi_Veri forfeited this round. 

Sadly, my opponent forfeited Round 3, but she should be back for a closing statement next round. Because the forfeit has deprived me of the ability to refute my opponent's next set of points within this debate itself, I would like to reserve the right to use one comment in the Comments section to refute any points that seem to be new to the debate.
Thanks, now let's wrap up this debate. "In conclusion, the fact that the first nine marbles were blue clearly supports the idea that the final marble will be blue. The color blue is an established color of marble, while red must first compete with yellow, green, purple, invisible, orange, and numerous others for being the unmentioned color." Vote CON. Vi_Veri forfeited this round. 
7 votes have been placed for this debate. Showing 1 through 7 records.
Vote Placed by quarterexchange 6 years ago
mongeese  Vi_Veri  Tied  

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Vote Placed by Vi_Veri 7 years ago
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Vote Placed by mongeese 7 years ago
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Vote Placed by RoyLatham 7 years ago
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It doesn't change the analysis very much when the bag has only ten marbles. We are characterizing the process used for filling the bag using the sample. The first nine were drawn at random, so they are a basis for statistically characterizing the population in the bag. Whatever process was used to fill the bag, it was very likely generating more blue marbles than nonblue ones for the bag. Therefore the resolution is false. It is true that the color of the tenth marble is uncertain, but the prior sample makes it more likely blue than nonblue.
Someone one commented that in physics the concepts are easy but the calculations are difficult, whereas in statistics the concepts are difficult but the calculation are easy.
But how do we come to that understanding of math. How do we come to know it??
Through discriminating things.
Now our understanding of Math is dependent upon our nature, and our understanding of reality is as well.
So claiming to understand the nature of reality presupposes that you understand your own nature, for which you need a framework (of greater reality) to understand it in.
Thus you begin talking about the Brain (our physical nature), But that rests upon a greater framework.
I find this to be circular. Reality= this; b/c our nature= that, which is dependent upon Reality=this
There's "this" and then "that". That makes 2 then there's "that too" which is three.
Math is just taking this and adding to it/understanding it better.
What?
"But I haven't ever run seen anything that would constitute "proof" of 3 dimensions. "
I gave you a start. You 'seeing' it isn't a prerequisite for it.
"If your claiming there is it'd be nice if you could give One example and sketch out how."
What aren't you getting about very nonvague hints about what you should be reading? :P
"I was talking more of why we think the three are what they appear to be, and will continue to be so."
Because dimensions don't disappear unless reality does. They are part of the fabric of reality. Sure mathematics can give us abstract extra dimensions, but they exist as equations. :)
I was talking more of why we think the three are what they appear to be, and will continue to be so.
But I haven't ever run seen anything that would constitute "proof" of 3 dimensions. (It would seem physics is based upon our understanding of 3D; not proof of it)
If your claiming there is it'd be nice if you could give One example and sketch out how.