EPTOn July 20 2013 02:09 Rassy wrote:
so 1/infinite times infinite is now 0 lol?
so 1/infinite times infinite is now 0 lol?
Your post is too vague for math, and outside of math has very little meaning.
Is the mind all chemical and electricity? - Page 93
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mcc
Czech Republic4646 Posts
Your post is too vague for math, and outside of math has very little meaning. | ||
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Rassy
Netherlands2308 Posts
(and its also what i did learn) Though its not according to several math grade people in this thread, parrallel universe amongst others. ( who said that if you pick a number between 0 and 1 an infinite amount of time, then you would still have 0 odds of picking a specific number) Maybe its all just a huge misunderstanding, meh. We should find a new subject to discuss tbh. | ||
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Reason
United Kingdom2770 Posts
On July 20 2013 02:17 mcc wrote: Your post is too vague for math, and outside of math has very little meaning. I think he was asking if (1/infinity)*infinity = 0 Kind of like if you told me (1/2)*2 wasn't = 1 I'd start freaking out... | ||
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Shiori
3815 Posts
On July 20 2013 02:21 Reason wrote: I think he was asking if (1/infinity)*infinity = 0 Kind of like if you told me (1/2)*2 wasn't = 1 I'd start freaking out... Well, it's definitely not necessarily true that (1/infinity)*infinity is 1. The problem here is that we have no real definition of infinity (or whether these two infinities have the same cardinality) or multiplication or even a field of numbers, so it's not clear what the answer to this question is. | ||
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Rhaegal
United States678 Posts
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Shiori
3815 Posts
On July 20 2013 02:25 Rhaegal wrote: This question always confused me. What the hell else could it be? A soul? I have decided that there is no way to answer the original question as stated without committing some form of begging the question. | ||
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Reason
United Kingdom2770 Posts
On July 20 2013 02:25 Rhaegal wrote: This question always confused me. What the hell else could it be? A soul? Yes? | ||
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Darkwhite
Norway355 Posts
Read Myrdraals last post in this topic. There are ample amounts of confusion and disagreement, so something has obviously gone wrong somewhere. I think different explanations involving less formalism would have avoided these misunderstandings, but I wouldn't mind hearing your take on this. The good thing about p=1/inf is that it preserves the intuition that, with a large enough sample size N, N*p != 0. Say we are making a function from all integers (Z) to the positive integers (N), by mapping each Z to a random number in N - let's not concern ourselves too much with picking something at random from an infinite set. For this function, what is the probability that any given Z maps to itself? This must obviously be something along the lines of 1/(2*inf) or zero - for any given Z, there is sort of a 50% chance that it is in N, and then a 1/(size(N)) chance that it maps to itself, and size(N) is sort of inf. The slight problem with denoting this probability as zero, is that it invites the (false) intuition that the function will have no such identity mappings at all - denoting it as zero disguises the non-impossibility of an identity mapping, if you aren't rigorously enough trained to know that infinities are difficult beasts. 1/inf keeps you alert that, with infinite candidates, depending on the sizes of the infinities in question, you might get either none or some or even an infinite amount of them. I think this is more or less why Myrdraal wanted to write the probability as 1/inf rather than 0, which I personally think is more than okay. I think the problem was everyone spent much more time proclaiming 1/inf as heresy than trying to understand what he was actually saying. | ||
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Rhaegal
United States678 Posts
On July 20 2013 02:27 Shiori wrote: I have decided that there is no way to answer the original question as stated without committing some form of begging the question. Exactly. It's like asking, "is a water molecule all Oxygen and Hydrogen?" | ||
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CoughingHydra
177 Posts
On July 19 2013 21:10 Tobberoth wrote: Maybe I misunderstood your post completely, but from I gathered, you proved that the probability of picking a single number between 0 and 1 is zero by making an interval between that single number and since a number minus that same number is 0, the probability is 0. I was just pointing out that this will obviously always be true. What's the probability of getting a 5 in the set you posted? 0, because 5-5 = 0. What I'm not getting is where you make the distinction between 0.47 - 0.47 compared to this 5-5 comparison. The reason why he could do that with choosing a number in [0,1] and couldn't do that with choosing a number in {1,2,3,4,5,6} lies within the result in measure theory, the Radon-Nikodym theorem. If you have two measures (here probability and Lebesgue measure - Lebesgue measure measures the lenght of an interval: l([a,b]) = b-a) and both satisfy certain conditions then you can express one measure with the other (although through integration). So I assume it can be shown that you can express the probability of picking a number within a set (subset of [0,1]) as a Lebesgue measure of said set (I haven't had a course in continuous probability yet, it's in the 4th/5th year of studying maths). | ||
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Shiori
3815 Posts
On July 20 2013 02:33 Darkwhite wrote: Shiori: Read Myrdraals last post in this topic. There are ample amounts of confusion and disagreement, so something has obviously gone wrong somewhere. I think different explanations involving less formalism would have avoided these misunderstandings, but I wouldn't mind hearing your take on this. The good thing about p=1/inf is that it preserves the intuition that, with a large enough sample size N, N*p != 0. Say we are making a function from all integers (Z) to the positive integers (N), by mapping each Z to a random number in N - let's not concern ourselves too much with picking something at random from an infinite set. For this function, what is the probability that any given Z maps to itself? This must obviously be something along the lines of 1/(2*inf) or zero - for any given Z, there is sort of a 50% chance that it is in N, and then a 1/(size(N)) chance that it maps to itself, and size(N) is sort of inf. The slight problem with denoting this probability as zero, is that it invites the (false) intuition that the function will have no such identity mappings at all - denoting it as zero disguises the non-impossibility of an identity mapping, if you aren't rigorously enough trained to know that infinities are difficult beasts. 1/inf keeps you alert that, with infinite candidates, depending on the sizes of the infinities in question, you might get either none or some or even an infinite amount of them. I think this is more or less why Myrdraal wanted to write the probability as 1/inf rather than 0, which I personally think is more than okay. I think the problem was everyone spent much more time proclaiming 1/inf as heresy than trying to understand what he was actually saying. I get what you're saying. I think the problem is that, while intuition is great, permitting writing 1/inf rather than 0 encourages a sort of informal way of thinking about probabilities, which leads people to equivocate between nonzero probability and how much of a "chance" there is of something. I mean, suppose we wrote 1/inf instead of probability zero for "almost never." Then, on the face of it, we'd have people saying that "well the chance is bigger than nothing so it's at least a chance" which is kinda fine, in a way, but it misrepresents what we actually mean when we say p(x)= 0 or p(x) = 1. | ||
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mcc
Czech Republic4646 Posts
On July 20 2013 02:21 Reason wrote: I think he was asking if (1/infinity)*infinity = 0 Kind of like if you told me (1/2)*2 wasn't = 1 I'd start freaking out... It is not clear what he means by infinity. The standard, outside of set theory infinity, used in schools is set up in such a way that 0 * infinity is not defined at all IIRC. So if we assume that 1/infinity is 0 , then (1/infinity)*infinity can be not defined at all. | ||
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Darkwhite
Norway355 Posts
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mcc
Czech Republic4646 Posts
On July 20 2013 02:27 Shiori wrote: I have decided that there is no way to answer the original question as stated without committing some form of begging the question. Only in the same way as no question about real world can be answered without some form of begging the question. The only way to stop the infinite train of those question is to agree on some basic assumptions. | ||
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mcc
Czech Republic4646 Posts
On July 20 2013 02:33 Darkwhite wrote: Shiori: Read Myrdraals last post in this topic. There are ample amounts of confusion and disagreement, so something has obviously gone wrong somewhere. I think different explanations involving less formalism would have avoided these misunderstandings, but I wouldn't mind hearing your take on this. The good thing about p=1/inf is that it preserves the intuition that, with a large enough sample size N, N*p != 0. Say we are making a function from all integers (Z) to the positive integers (N), by mapping each Z to a random number in N - let's not concern ourselves too much with picking something at random from an infinite set. For this function, what is the probability that any given Z maps to itself? This must obviously be something along the lines of 1/(2*inf) or zero - for any given Z, there is sort of a 50% chance that it is in N, and then a 1/(size(N)) chance that it maps to itself, and size(N) is sort of inf. The slight problem with denoting this probability as zero, is that it invites the (false) intuition that the function will have no such identity mappings at all - denoting it as zero disguises the non-impossibility of an identity mapping, if you aren't rigorously enough trained to know that infinities are difficult beasts. 1/inf keeps you alert that, with infinite candidates, depending on the sizes of the infinities in question, you might get either none or some or even an infinite amount of them. I think this is more or less why Myrdraal wanted to write the probability as 1/inf rather than 0, which I personally think is more than okay. I think the problem was everyone spent much more time proclaiming 1/inf as heresy than trying to understand what he was actually saying. On the contrary, all the confusion is caused by too little formalism as everybody sees something different behind the same symbols. | ||
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Darkwhite
Norway355 Posts
On July 20 2013 03:15 mcc wrote: On the contrary, all the confusion is caused by too little formalism as everybody sees something different behind the same symbols. It would've been easier if everybody had a university level degree in mathematics, but pretending won't make it so. | ||
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Shiori
3815 Posts
On July 20 2013 03:13 mcc wrote: Only in the same way as no question about real world can be answered without some form of begging the question. The only way to stop the infinite train of those question is to agree on some basic assumptions. The OP said: To be more exact - is the mind, in all its complexity, physical, the is, the chemical and electric networks in the brain? What about morality, love, ideas, empathy, compassion, imagination? Are these mere byproducts of physiological processes that are in a way similar to the chemical and electrical impulses experienced by other animals? To me, this is inescapably pretty much question begging, because whether or not "morality, love, ideas, empathy, compassion, imagination" are physical depends entirely on what you define those thing to be. In addition, "the mind" is a totally nebulous concept because nobody can concisely define what they mean the noun to mean without inevitably forgetting to include some ineffable piece of experience. "Minds" are honestly probably the only thing that human beings are in no real position to analyze because it's impossible to separate our experience of our own mind from the thing itself, and physicalism, whether or not it's true, seems doomed to being a trivial result either way, as I don't think it's possible for human beings to reductively perceive of minds in any intuitive sense, simply because reductionism about minds deconstructs perception and intuition themselves. I'm not saying that reductionism is false (I don't even know that reductionsim is necessarily possible to evaluate) but I am saying that strikes me as impossible for any human being to grasp, on any deep level, a reductive account of their own mind. I have no real proof of this, other than that it strikes me as being implausible. | ||
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Rassy
Netherlands2308 Posts
At least not where i grew up, we dealth with this in 2nd or 3rd grade highschool age 14/15, but meh. will stop posting on this subject. | ||
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DoubleReed
United States4130 Posts
On July 19 2013 21:10 Tobberoth wrote: Maybe I misunderstood your post completely, but from I gathered, you proved that the probability of picking a single number between 0 and 1 is zero by making an interval between that single number and since a number minus that same number is 0, the probability is 0. I was just pointing out that this will obviously always be true. What's the probability of getting a 5 in the set you posted? 0, because 5-5 = 0. What I'm not getting is where you make the distinction between 0.47 - 0.47 compared to this 5-5 comparison. I was talking about length of intervals. If you want to do that over discrete sets, you can. But you have to develop a different type of measure. In that specific case, each point would probably have 1/6 measure. When you're doing probability over the real line, you use Lebesgue Measure, which for intervals is the same thing as b - a. If you're not doing intervals, or if you're not doing probability over the real line (or if you're doing something weird), then it's not the same. Likewise, the length of the set [0,1] U [2,3] is 2. Even though doing b - a would yield 3 - 0 = 3. Well it's just because it's not an interval. | ||
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koreasilver
9109 Posts
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