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#1 |
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Picky V. Nitty
Join Date: Aug 2010
Location: Southern California
Posts: 2,441
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Can Science or Math Provide Evidence for a Common Sense Conclusion?
Can science or math provide evidence for a common sense conclusion? I am just curious, there's no real issue involved.
I am looking for a specific piece of paper (target), which is in one of three piles of papers. Pile A is smallest, Pile B is medium-sized, and Pile C is biggest. Pile A is less than half the size of Pile B. Piles A and B together are less than half the size of Pile C. Common sense (as I see it) says to start looking in Pile A, then Pile B, and look in Pile C last. This way you look through the least amount of paper before finding the target. I started to wonder if there is a way to reach this conclusion scientifically or mathematically. Is this question "outside the realm" of science and/or math? Or is it a really simple science/math answer that I should have seen immediately (if I weren't so deficient in science and math knowledge )?
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You can't teach an old dogma new tricks -- Dorothy Parker The sceptics continued to look sceptical and the believers believing -- Catherine Aird Proud member of SCOFF (SoCal Opposing Feline Filleting) |
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#2 |
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Penultimate Amazing
Join Date: Nov 2004
Location: Philadelphia, PA...USA
Posts: 14,482
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I assume you are going to look through the papers and stop when you find the one you are looking for. If that is the case, it doesn't matter which pile you start with. If you started with Pile C and found your paper 2nd from the top, you'd stop immediately.
Edit: Are you suggesting there is a copy of the target paper in each pile? If so, statistics says start with Pile A. |
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If man came from dust, why is there still dust? |
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#3 |
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Philosopher
Join Date: Sep 2007
Location: Denver, Colorado
Posts: 6,605
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Why would that be? What if the target paper is on top of pile C? I think the common sense here comes in not because you feel one pile is more likely to have the target than the others, nor because statistically searching the small piles is better than searching the others.
It is because you have three piles to keep track of, to keep organized, and that take up space on your table. If you can quickly move through some smaller piles, you can pile them out of the way and make space for other things, like lunch. Or realizing halfway through your search you need to organize the papers in new piles for some other reason. Resolving the small piles first makes room for other contingencies. I think the gut-feeling to organize that way is at the basis of what feels like the common sense way of planning your search, in this example. |
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#4 |
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Picky V. Nitty
Join Date: Aug 2010
Location: Southern California
Posts: 2,441
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No, there is only one target paper and I'll stop when I find it. Why does it not matter which pile I start with? Is this because there is no way to know where the target is? This means my problem is that my "common sense" conclusion is incorrect, but I don't see why.
I would think starting with the smallest group would mean: if the target is in Pile A, I've looked through the minimum amount of paper; if the target is in Pile B, I've looked through an amount of paper less than Pile C; if the target is in Pile C, I've looked through more paper than I needed to, but not a lot more. So starting with Pile A would make sense. Why is this wrong? |
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You can't teach an old dogma new tricks -- Dorothy Parker The sceptics continued to look sceptical and the believers believing -- Catherine Aird Proud member of SCOFF (SoCal Opposing Feline Filleting) |
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#5 |
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Philosopher
Join Date: Jul 2007
Posts: 6,872
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Assuming there is no difference in how long it takes you to verify a given paper is not what you are looking for then it clearly doesn’t matter where you start. While you can search the smallest pile most quickly, the paper you are looking for has the least chance to be there. No matter how many piles you have you still need to look (on average) though the same number of papers to fine the one you want.
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"Anything's possible, but only a few things actually happen" |
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#6 |
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Banned
Join Date: Sep 2010
Location: Here
Posts: 2,279
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sure.
identify what the 'common sense' is and have your goal. i ground the 'global' common sense to life. ie.. all that lives, intends to keep doing it, naturally (via instinct or choice). Now what is your common sense pursuit? Then maybe we can assist with digging thru less piles of doodoo you may be required to meander thru to find, that ONE.
Quote:
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#7 |
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Master Poster
Join Date: Nov 2002
Posts: 2,398
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It is wrong if the whereabouts of the paper are completely random. If it's completely random it has the same chance of being in the A-sized top part of pile C, the A-sized top part of pile B or the A-sized pile A. Or a top part half that size for that matter.
Unless there are further constraints such as "the paper is more likely to be towards the bottom of the pile" or, as previously mentioned, it's equally likely to be in any _pile_ rather than being in a random part of the stack, it doesn't matter which stack you start with. If you start with pile A you'll be more likely to look through the whole stack than if you start with pile C, so the total size doesn't matter. Your "common sense" idea might be related to the often wrong assumption that given two different circumstances, either has a 50% chance of occuring. You're assuming either that the paper has an equal chance of being in in pile A, B or C, or that you have to look through all of whichever pile you start with, or both. Assumptions that may or may not be true, but are certainly not common sense. |
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Well, I DON'T CARE WHAT YOU LIKE TO BELIEVE, GODDAMMIT! I DEAL IN THE FACTS! -Cecil Adams |
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#8 |
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Illuminator
Join Date: Mar 2008
Posts: 4,178
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I think FattyCatty made an unstated assumption that the target paper is equally likely to be in any of the three piles. In that case her "common sense" solution is correct. But if probability of the paper being in a given pile is proportional to pile's size, then it does not matter on which you start.
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Gamemaster: "A horde of rotting zombies is shambling toward you. The sign over the door says 'Accounting'" |
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#9 |
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Philosopher
Join Date: Dec 2004
Location: Flatland
Posts: 5,307
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No, it isn't outside the realm of mathematics. There are various searching algorithms designed to minimize the search time/steps given various different starting assumptions.
For example, if the paper you are searching for has an equal likelihood of being in any particular pile, then starting with pile A will minimize search time over many iterations of the problem. On the other hand, if the probability of each pile is based on the number of papers in each one, then it won't make any difference which pile you start with, the average search time won't vary depending on which pile you start with. Pile A will have the lowest probability of success because it has the least number of papers that might possibly be your target, but it will also take the least amount of time to search. |
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Beth "You are not the stuff of which you are made." Richard Dawkins, July 2005, 10:45 http://www.ted.com/talks/richard_daw..._universe.html |
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#10 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#11 |
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Guest
Join Date: Sep 2009
Posts: 11,853
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As has been previously stated, determining whether or not your common sense approach matches reality requires determining which of the following statements are more accurate:
1) Of all the pieces of paper amongst all three piles, each individual piece of paper is equally likely to be the target piece of paper. 2) Of the three piles, each pile is equally likely to contain the target piece of paper. If #1 is true, then it doesn't matter what pile you start looking in (but see the Addendum below). The #2 is true, then always begin with the smallest pile, as each piece of paper in the smallest pile is more likely to be the target piece than each piece of paper in a larger pile. Addendum: If you derive any value just for finishing a pile, then it makes sense to search the smallest pile first even in case #1. For example, if getting through a pile gives you a sense of accomplishment, or makes you think "I'm 1/3 done," or allows you to move that full pile off your desk (someone else mentioned this above), then start with A. As the smallest pile, A allows for you to derive value in finishing a pile with the least expenditure of search time. |
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#12 |
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Opinionated Jerk
Moderator Join Date: Jul 2006
Location: New York
Posts: 11,885
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If the one sheet of paper is equally likely to be anywhere in any pile, probabilistically, it does not matter where you start. Let's say there are a hundred papers:
Pile A has 10 papers, 10% of the total. Pile B has 30 papers. Pile C has 60 papers. It's fastest to exclude Pile A, because you're only searching 10% of the papers. But you've only got a 10% chance of finding the paper you're looking for. Now, imagine you start with pile C but choose, for your own reasons, to only examine the first ten pages of pile C. You have examined the same 10% of the total and have the same 10% chance of finding your paper. The size of the piles is an arbitrary condition you're imposed on the papers. Probability doesn't care about your piles. |
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Follow me on Twitter! @LossLeader This force is receiving all the right to vote through the use of magic. - Miernik Wieslaw <NEW> VOTE FOR ME JUST BECAUSE <NEW> |
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#13 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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Which is why the stated "common sense" solution in this example is NOT correct.
There is no greater probability the wanted paper is in any of the three stacks. And if you put the wanted paper in one stack first then divided the one stack into three stacks of unequal size, the probability would be proportioned according to the size of the stacks. There would actually be a greater probability the wanted paper was in the biggest stack. But the question is not about looking in the fewest number of stacks, the issue is finding it looking at the fewest number of papers. |
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#14 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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BTW, my answer comes from my "common sense" analysis of the problem, so I would argue with the OP premise that "common sense" suggests one look in the smallest stack. Common sense is really another way of saying one's knowledge and experience to that point. What may seem like some magical brain function, "common sense", is really much more complex than it appears superficially.
Our brains have a certain organizational structure and a basic inherent logic that comes from our genetics. From there we build within that initial frame work to arrive at our "common sense". What many people fail to realize is just how much nearly instantaneous sub-conscious brain activity goes into those common sense determinations. |
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#15 |
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Master Poster
Join Date: Jun 2010
Posts: 2,567
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I don't believe in common sense.
I find that when people say something is common sense, they are just referring to something that they have known for a long time, or else something that is a cultural norm for their area. Something that is common sense should be a truism that is intuitively grasped by everyone. I can't really think of anything that meets that definition. People are often mislead by their intuition. In this case, King Merv cut right to the heart of it. the three piles essentially amount to one large pile for all practical purposes. The question could be rephrased as "Should I start looking on the top, in the middle, or at the bottom of the pile?" The answer is that assuming a random placement of the paper, it doesn't matter. The "common sense" answer has lead us astray. That's my rant on common sense. ![]() Regards, Canis |
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"...The chief deficiency I see in the skeptical movement is its polarization: Us vs. Them -- the sense that we have a monopoly on the truth; that those other people who believe in all these stupid doctrines are morons; that if you're sensible, you'll listen to us; and if not, to hell with you. This is nonconstructive. It does not get our message across. It condemns us to permanent minority status." - Carl Sagan
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#16 |
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Picky V. Nitty
Join Date: Aug 2010
Location: Southern California
Posts: 2,441
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Thank you everyone for your response to my question. I guess I didn't make it clear that these are actual piles of the actual proportions I gave in the OP, and that there is an actual "target" paper that I am looking for. I just don't remember which pile I put it in, silly me.
So I will start my "actual" search with Pile A because it is smaller and will go faster, and because I can put it aside sooner and clear my desk a little. Thank you again for all the responses. I'll try to be more careful with my assumptions in the future, especially in assuming something is common sense. I'll post when I find the target paper to say which pile it was in. |
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You can't teach an old dogma new tricks -- Dorothy Parker The sceptics continued to look sceptical and the believers believing -- Catherine Aird Proud member of SCOFF (SoCal Opposing Feline Filleting) |
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#17 |
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Master Poster
Join Date: Jun 2010
Posts: 2,567
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Yes please do so!
![]() This is an interesting thread and i would love to hear about the outcome. |
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"...The chief deficiency I see in the skeptical movement is its polarization: Us vs. Them -- the sense that we have a monopoly on the truth; that those other people who believe in all these stupid doctrines are morons; that if you're sensible, you'll listen to us; and if not, to hell with you. This is nonconstructive. It does not get our message across. It condemns us to permanent minority status." - Carl Sagan
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#18 |
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Banned
Join Date: Sep 2010
Location: Here
Posts: 2,279
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That is funny! the superficial part comes from the variety of definitions (far too much is subjective when the overall objective, is life)
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what a fricken crack up? That is like suggesting an american is born free but not a palestinian. Our glial records memories and our brain offers a coherance of experienced memories-knowledge. The part that is genetic, is honestly representing what we have experienced (no false witness), naturally. A subjective discipline is learned. A capacity to create BS from experienced knowledge is a choice of a conscious mind to divert from what is real. Instinctly, life intends to live, no matter what you believe.
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A method to prove his inquiry are the 'diversity of religious adherance'.... most all 'sense' of belief is grounded in a common sense to live longer. Religions exists that are supposedly offering the venue to live longer. Take up the science pile, the stack may be bigger but i promise you will find what more to enable commmon sense, then any other pile. But then for the simple; 'do unto others as you would have them do unto you'. (that be the short stack) Which 'common sense' is being sought? Life, the truth, reality or just where to find the ignor button?
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uncommon sense; there is no such thing as a perfect vacuum anywhere within the universe (between any 2 points of mass). Rational sense, we all will sleep, eventually. Unwanted sense (reality up front); all memories are affixed to the body (nothing goes anywhere with anyone, after our period of choice) And the proof is ask any alzheimers patient as often they are having to be re-introduced to their own children. (but still conscious of life) Lots of cute ideas on this thread. Can common sense be proven mathematically? i think so. If the common sense is grounded to the common goal of all life; to live. Basic |
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#19 |
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Illuminator
Join Date: Jul 2006
Posts: 4,658
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Aha. So that does suggest that the intial probabilities are "it's got a 1/3 chance of being in pile A, a 1/3 chance of being in B," etc. (As opposed to, "There are 1000 pieces of paper total, each of which has a 1/1000 chance of being the target") Under the actual assumption: yes, start with the smallest pile.
This is a problem amenable to math, although not much appeared in this thread. |
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#20 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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This is the same as the problem of Let's make a Deal, what is behind doors 1,2 & 3.
You start with a 33% chance of finding the desired paper in each stack, just as Avalon XQ has noted, there is the same chance you'd find the paper 10 pieces down in the largest stack as you would find it 10 pieces down in the smallest stack. But once you eliminate one stack, now you have 50% chance of finding the paper in either stack, but you eliminated 33%, so your odds become 50% of 66% (no paper) vs 50% of 33% (paper). In the Monty Hall problem, however, it depends on Hall eliminating a booby prize prize door. The question is, should the contestant change their initial choice and the answer is, yes. But how does that apply in this case? While there is a 33% chance of finding the paper in the smaller stack, and therefore it appears you'd have a higher chance of finding it going through fewer papers, the probability of finding finding it in either remaining stack once you eliminate the first stack changes. So you start with a 33% chance of finding it in stack #i that has 10 papers. You have a smaller chance of finding it in the first 10 papers of stacks 2 and 3. But your chances of finding it in any of the three stacks was the same. If you do not find the paper in stack number 1, now the odds of finding it in stacks 2 & 3 increase. It's my understanding the odds become a wash overall. And my "common sense" logic says the paper is going to be found after looking through 'x' number of papers regardless of which order you look through the papers. I do not claim that my common sense is correct here, just that it seems correct to me. If I'm wrong, I'll learn something new. |
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#21 |
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Illuminator
Join Date: Apr 2009
Posts: 3,721
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#22 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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__________________
(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#23 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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Your declaration of what was "common sense" to you was not an error. I was just saying that "common sense" is not a fixed thing. The same is true when people refer to "intuition". Both intuition and common sense involve a lot of under the radar and very fast brain activity. It is an individual thing, not a universal thing. But it still exists.
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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#24 |
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Sole Survivor of L-Town
Join Date: Dec 2005
Location: Wilson, North Carolina, USA, Earth
Posts: 11,330
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My "common sense" tells me that it will always be in whichever pile I look in last. Probably at the bottom. That or it will be second from the top on the first pile I look in, but will stick to the paper on top, so that I don't find it until a 2nd pass through the piles.
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Religion and sex are powerplays. Manipulate the people for the money they pay. Selling skin, selling God The numbers look the same on their credit cards. |
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#25 |
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Philosopher
Join Date: Jul 2007
Posts: 6,872
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Again though it doesn’t matter if they are actual sizes or actual piles what matters is the chance that the document will be in a given pile. If the piles are random then the chances that the document is in any given pile is always the inverse of the number of documents in the pile. This means searching the smallest pile is fastest, but also the least likely to succeed and two exactly offset.
If the piles are not random then the change to find vs time to search will not be the same for each pile and there could be an optimal pile to search first but one could come up with scenarios that favour any of the piles. Your description is too vague, so we don’t have enough information to know which one is best to search first so we default to assumption the piles are random which means it doesn’t matter where you start. Now, if you were to say something like “I know it’s as likely to be in Pile A as it is to be in Pile B”, then yes you search the smaller pile first. I suspect, however, that you are basing you’re common sense assessment on this assumption without knowing if it’s true or not, which can be a common reason why common sense fails. |
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"Anything's possible, but only a few things actually happen" |
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#26 |
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Banned
Join Date: Sep 2010
Location: Here
Posts: 2,279
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you said: Quote: Our brains have a certain organizational structure and a basic inherent logic that comes from our genetics. and that is a joke, right? you were being funny, right? knowledge is learned. The only LOGIC is the ability to honestly represent what has been learned/experienced. The first boob we eat from, taught us.. 'food' ... to sustain the 'life' ........... that is the inherant goal of 'all life'. The ability to use common sense, needs common sense to honesty over rules beliefs and the ever evolving misconceptions of opinion. I pointed out, that your opinion was funny! Directly put! if you have a question on my opinion, then ask a coherant question. otherwise, you are rambling on |
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#27 |
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Master Poster
Join Date: Jun 2010
Posts: 2,567
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Good Grief! How does a fun little thread like this turn into an argument!?
Does every thing have to be a big urination contest in this forum!? I swear I am about done with it. |
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"...The chief deficiency I see in the skeptical movement is its polarization: Us vs. Them -- the sense that we have a monopoly on the truth; that those other people who believe in all these stupid doctrines are morons; that if you're sensible, you'll listen to us; and if not, to hell with you. This is nonconstructive. It does not get our message across. It condemns us to permanent minority status." - Carl Sagan
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#28 |
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Penultimate Amazing
Join Date: Feb 2008
Location: Belgium (Flatland)
Posts: 31,477
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#29 |
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Sole Survivor of L-Town
Join Date: Dec 2005
Location: Wilson, North Carolina, USA, Earth
Posts: 11,330
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Religion and sex are powerplays. Manipulate the people for the money they pay. Selling skin, selling God The numbers look the same on their credit cards. |
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#30 |
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Banned
Join Date: Sep 2010
Location: Here
Posts: 2,279
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#31 |
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Dart Fener
Join Date: Aug 2002
Location: The Lando System
Posts: 2,396
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my nerdy sports blog: betting market analytics |
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#32 |
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Cythraul Enfys
Join Date: May 2006
Posts: 28,961
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As I have noted in several places whilst reading neatly rational data from others, Bishadi appears to lack the ability to write English that is either clear or concise. Thus I have requested multiple times whether English is his first language (I do not believe it can be given his phrasings). So far I have seen no reponse and, as best I can tell, none has been made.
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There is no problem so great that it cannot be fixed by small explosives carefully placed. Wash this space! We fight for the Lady Babylon!!! |
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#33 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,099
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The realistic answer I think depends on how it got there: ie. did you have three piles to choose from, and simply put it in one, but forgot which one? That sounds like its the case, and if so, start with pile A.
For instance, if you had three piles, and piles B and C are larger simply because they've been around longer, but you know that A was present when you put the paper down, then I'd imagine that the probability that it's in A, B, or C are all approximately equal. On the other hand, if you had one large pile (within which you have no idea where the paper was) and you split it into three smaller piles, A, B and C, then it doesn't matter which pile you start with. Though in that case the "getting the pile off my desk" is a separate issue worth consideration. Point being, there are some missing details in the OP that we need to determine the answer. You may not know those details explicitly, but they may be implicit in other details left out (like the ones supplied in a later post when you said you weren't sure which of the piles you'd put it in, which implies that you did put it with equal probability into one of the piles). |
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#34 |
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Penultimate Amazing
Join Date: Mar 2003
Location: Central Illinois
Posts: 34,729
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Hell, dynamiting fish in a barrel is more challenging. - Ladewig I suspect you are a sandwich, metaphorically speaking. -Donn And a shot rang out. Now Space is doing time... -Ben Burch You built the toilet - don't complain when people crap in it. _Kid Eager |
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#35 |
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Muse
Join Date: May 2009
Location: Lansing, MI
Posts: 835
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#36 |
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Banned
Join Date: Oct 2007
Posts: 20,454
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Assuming 100 sheets of paper, the most one needs to look at is 99 sheets, to know where the one is.
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#37 |
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Picky V. Nitty
Join Date: Aug 2010
Location: Southern California
Posts: 2,441
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Again, thank you everyone for your responses to my question. I started my search with Pile A, no target found; proceeded to Pile B; no target found; with a sigh, I tackled the dreaded Pile C, assuming it was now just a matter of about 15 minutes before I found my target paper.
To my chagrin, I got to the end of the pile without finding it. Oh no, I wailed, ZirconBlue was right and I'll have to do a second pass through all the papers. So, good little procrastinator that I am, I decided I'd tackle the job "in a little bit." A little later, while doing something else, I moved a booklet on top of the file cabinet beside the desk. And what to my wondering eyes did appear, but my target paper! ![]() Emotions raced in circles through my brain: relief at finding it, embarrassment at starting a thread based on a totally wrong assumption, resentment toward the paper for not being where I expected, bewilderment at my false memory of placing it in a pile of papers on my desk. I now feel like a complete fool and a waster of everyone's time. I apologize. And I definitely will be more careful about my assumptions in the future. And about starting threads based on those assumptions. ![]() Although I am going to start a thread on an interesting news item - does that count? |
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__________________
You can't teach an old dogma new tricks -- Dorothy Parker The sceptics continued to look sceptical and the believers believing -- Catherine Aird Proud member of SCOFF (SoCal Opposing Feline Filleting) |
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#38 |
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Banned
Join Date: Oct 2007
Posts: 20,454
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Not good enough!
I demand blood! |
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#39 |
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formerly skeptigirl
Join Date: Feb 2005
Location: Shifting through paradigms
Posts: 40,628
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It's not a joke and you need to stop feeling superior and think about what someone is saying before you get so cocky.
Yes, we learn. But the brain is not a blank slate to start with. It has a specific way of organizing information and a specific way it assesses that information. For example, we have a natural genetic function of seeing patterns, especially what we believe are cause and effect patterns. One can learn to modify this. So when I give someone who hasn't modified their pattern a flu shot, and they get sick the next day, they are convinced the flu shot caused the symptoms. But someone who has learned not to jump to false conclusions knows to test that assumption. So we give 100 people randomly assigned flu shots and fake shots (saline) and see who gets sick. If the same number of people get sick in each group, it was not due to the flu shot. Other things one's brain does naturally is how it organizes patterns it recognizes. When you see a tree species you've never seen before, you don't have to learn that it is a tree. Your brain has a pattern recognition system built in that established a tree pattern. You recognize the new tree species is a tree nearly instantaneously. But in reality, your brain had to perform a pattern recognition calculation for you to recognize that tree. We have an innate brain capability to learn language. It changes over time. So an infant learns certain sounds and by a couple years, learns the language. Years later that brain function deteriorates. You can still learn a new language as an adult, but it is harder and is learned differently than a toddler learns. And, it's really hard to learn the actual sounds after a certain age. It's why I cannot roll my Rs and many Spanish speaking people cannot pronounce "girl" very well. You are thinking of the brain as some kind of blank slate, but you are failing to consider even a blank slate has a structure to begin with. And so does our brain. |
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(*Tired of continuing to hear the "Democrat Party" repeatedly I've decided to adopt the name, |
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Picky V. Nitty
Join Date: Aug 2010
Location: Southern California
Posts: 2,441
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I had a little nose bleed last night and will be happy to send you my used KleenexTM.
Just let me know the address. I can't send you my life's blood, as I already owe that to someone else.The only other thing I can offer is abject crawling, but I'd rather not, as it's so hard to get up and down. But if you insist, I will.
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You can't teach an old dogma new tricks -- Dorothy Parker The sceptics continued to look sceptical and the believers believing -- Catherine Aird Proud member of SCOFF (SoCal Opposing Feline Filleting) |
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