|
On July 16 2013 03:28 zefreak wrote:Show nested quote +On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously
Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_-
|
On July 16 2013 03:39 corumjhaelen wrote:Show nested quote +On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_-
There is already enough people saying random shit, excuse me to not make the difference if you don't mean it.
|
On July 16 2013 04:07 DertoQq wrote:Show nested quote +On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it.
Take things a bit less seriously, especially on the internet. You'll see, your life will seem better.
|
On July 16 2013 04:18 corumjhaelen wrote:Show nested quote +On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:On July 16 2013 02:39 corumjhaelen wrote:Now I think we should all start giving our opinions on P=NP and vote on what we like the most. I have a fun proof for those who like that sort of things. Credit to Hubert Chen : + Show Spoiler +
"Proof by contradiction. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified in polynomial time by a competent computer scientist, the existence of which we assert. However, since P=NP, the proof y can be generated in polynomial time by such computer scientists. Since this generation has not yet occurred (despite attempts by such computer scientists to produce a proof), we have a contradiction."
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better.
Do you have a degree to back up such a statement?
|
On July 16 2013 04:43 TSORG wrote:Show nested quote +On July 16 2013 04:18 corumjhaelen wrote:On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:On July 16 2013 02:44 LegalLord wrote:
[quote]
That is not how mathematics works. Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better. Do you have a degree to back up such a statement?
As someone with a degree in Statements, I can confirm his statement.
|
On July 16 2013 04:46 Shiori wrote:Show nested quote +On July 16 2013 04:43 TSORG wrote:On July 16 2013 04:18 corumjhaelen wrote:On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:On July 16 2013 03:00 corumjhaelen wrote:
[quote]
Really ? I'm like, really really surprised. Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better. Do you have a degree to back up such a statement? As someone with a degree in Statements, I can confirm his statement.
As someone with a degree in Degree Verification, I can confirm this is a real degree and I happen to know he is a leader in the field.
|
On July 16 2013 05:00 Reason wrote:Show nested quote +On July 16 2013 04:46 Shiori wrote:On July 16 2013 04:43 TSORG wrote:On July 16 2013 04:18 corumjhaelen wrote:On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:
[quote]
Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better. Do you have a degree to back up such a statement? As someone with a degree in Statements, I can confirm his statement. As someone with a degree in Degree Verification, I can confirm this is a real degree and I happen to know he is a leader in the field.
shit nvm!
|
On July 16 2013 05:00 Reason wrote:Show nested quote +On July 16 2013 04:46 Shiori wrote:On July 16 2013 04:43 TSORG wrote:On July 16 2013 04:18 corumjhaelen wrote:On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:On July 16 2013 03:10 LegalLord wrote:
[quote]
Not finding a proof yet does not imply that such a proof does not exist. Sometimes it does in physics, but never in mathematics. Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better. Do you have a degree to back up such a statement? As someone with a degree in Statements, I can confirm his statement. As someone with a degree in Degree Verification, I can confirm this is a real degree and I happen to know he is a leader in the field.
I have a degree in Bullshit Studies, but it's from Liberty University so it isn't worth much.
|
On July 15 2013 20:06 CoughingHydra wrote:Show nested quote +On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible'  Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen.
Eh. If P(A) = 1 = P(Ω) then P(A*) = 0 = P(∅), where omega is the full sample space and * denotes the compliment.
The thing with "random, nonrepeating" is not that your argument is wrong; it's that we can't (and might never be able to) prove that pi is random and normal.
To quote wikipedia: + Show Spoiler +The digits of π have no apparent pattern and pass tests for statistical randomness including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often.[16] The hypothesis that π is normal has not been proven or disproven.[16] Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found.
|
On July 16 2013 06:12 neptunusfisk wrote:Show nested quote +On July 15 2013 20:06 CoughingHydra wrote:On July 15 2013 19:57 Reason wrote:On July 15 2013 19:51 Umpteen wrote:On July 15 2013 19:41 Reason wrote:
If Pi is infinite and never repeating how could it not contain all possible integer sequences? Imagine it was infinite and never repeating but didn't contain the digit '7'. That's the problem with infinity: it doesn't necessarily mean 'everything possible' Okay, so there's 10 digits. 1. What is the probability of 7 not appearing in a random, non repeating sequence of 10 digits? 2. What is the probability of 7 not appearing in a random, non repeating sequence of 100 digits? 3. What is the probability of 7 not appearing in a random, non repeating infinite sequence of digits? I'd maintain the answer to 3. is zero. 7 must appear in a random, non repeating infinite series of digits because as the number of digits in the sequence approaches infinity the probability of 7 not appearing approaches zero. I'm sure similar argumentation for 0.9999999... = 1 could be used to demonstrate this? I'm not a mathematician in the slightest so sorry if that's a family sized bucket of stupid. If the probability is zero, that doesn't mean it can't happen, same in when the probability is 1, it doesn't mean it will happen. Eh. If P(A) = 1 = P(Ω) then P(A*) = 0 = P(∅), where omega is the full sample space and * denotes the compliment. The thing with "random, nonrepeating" is not that your argument is wrong; it's that we can't (and might never be able to) prove that pi is random and normal. To quote wikipedia: + Show Spoiler +The digits of π have no apparent pattern and pass tests for statistical randomness including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often.[16] The hypothesis that π is normal has not been proven or disproven.[16] Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found.
Bit late to the party yo.
+ Show Spoiler +better late the never 
Can you elaborate on this, perhaps?
"Eh. If P(A) = 1 = P(Ω) then P(A*) = 0 = P(∅), where omega is the full sample space and * denotes the compliment."
On July 16 2013 05:23 DoubleReed wrote:Show nested quote +On July 16 2013 05:00 Reason wrote:On July 16 2013 04:46 Shiori wrote:On July 16 2013 04:43 TSORG wrote:On July 16 2013 04:18 corumjhaelen wrote:On July 16 2013 04:07 DertoQq wrote:On July 16 2013 03:39 corumjhaelen wrote:On July 16 2013 03:28 zefreak wrote:On July 16 2013 03:24 DertoQq wrote:On July 16 2013 03:11 corumjhaelen wrote:
[quote]
Tell me more. Are you romanian ? Are you implying that every single proof possible to verify in polynomial time have been found yet ? Even if a program can verify a proof in a polynomial time, you still have to write and find this program. It was a joke and you are taking it seriously Naaaah, I was about to use an argument of authority and talk about my maths background to see where I could take them -_- There is already enough people saying random shit, excuse me to not make the difference if you don't mean it. Take things a bit less seriously, especially on the internet. You'll see, your life will seem better. Do you have a degree to back up such a statement? As someone with a degree in Statements, I can confirm his statement. As someone with a degree in Degree Verification, I can confirm this is a real degree and I happen to know he is a leader in the field. I have a degree in Bullshit Studies, but it's from Liberty University so it isn't worth much.
I'm sorry, that is not a real degree. Please take discussion more seriously in future, I expected more from you... t.t
|
On July 16 2013 06:14 Reason wrote:Show nested quote +On July 16 2013 06:12 neptunusfisk wrote:Eh. If P(A) = 1 = P(Ω) then P(A*) = 0 = P(∅), where omega is the full sample space and * denotes the compliment. The thing with "random, nonrepeating" is not that your argument is wrong; it's that we can't (and might never be able to) prove that pi is random and normal. To quote wikipedia: + Show Spoiler +The digits of π have no apparent pattern and pass tests for statistical randomness including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often.[16] The hypothesis that π is normal has not been proven or disproven.[16] Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found. Bit late to the party yo. + Show Spoiler +better late the never Can you elaborate on this, perhaps? "Eh. If P(A) = 1 = P(Ω) then P(A*) = 0 = P(∅), where omega is the full sample space and * denotes the compliment."
The sample space is the set of every possible outcome and the compliment of a set is everything that's not in the set, in this case the compliment of the sample set is the empty set.
If A is an event with probability exactly equal to 1, then by all means it is what will happen. The problem here is not in the math, it is in how well the model corresponds to whats being modelled.
|
How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there?
The example given was what is the probability of picking a specific real number between 0 and 1. It's 0 (almost never)
Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure).
I know it's not proven than Pi is actually this type of sequence, although it appears to be.
|
On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure).
I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems.
I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened.
But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here.
|
I confirmed this the first time I did LSD..
|
On July 16 2013 06:58 neptunusfisk wrote:Show nested quote +On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here.
Throwing a dart
For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable.
Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal.
The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain.
So.... do you prefer arsenic or cyanide?
|
On July 16 2013 07:15 Reason wrote:Show nested quote +On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide?
The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time.
|
On July 16 2013 07:23 neptunusfisk wrote:Show nested quote +On July 16 2013 07:15 Reason wrote:On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide? The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time.
Sorry, I was only covering probability = 0. You do realise I'm just copy pasting all this stuff right lol? Here's P = 1.
http://en.wikipedia.org/wiki/Almost_surely#Tossing_a_coin
|
On July 16 2013 07:34 Reason wrote:Show nested quote +On July 16 2013 07:23 neptunusfisk wrote:On July 16 2013 07:15 Reason wrote:On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide? The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time. Sorry, I was only covering probability = 0. You do realise I'm just copy pasting all this stuff right lol? Here's P = 1. http://en.wikipedia.org/wiki/Almost_surely#Tossing_a_coin
This article does a pretty poor job of covering what it means for a probability to converge to 1.
The probability isn't actually necessarily 1, it converges to 1 under certain conditions.
e: or 0 or any other probability, for that matter
|
On July 16 2013 09:29 wherebugsgo wrote:Show nested quote +On July 16 2013 07:34 Reason wrote:On July 16 2013 07:23 neptunusfisk wrote:On July 16 2013 07:15 Reason wrote:On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide? The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time. Sorry, I was only covering probability = 0. You do realise I'm just copy pasting all this stuff right lol? Here's P = 1. http://en.wikipedia.org/wiki/Almost_surely#Tossing_a_coin This article does a pretty poor job of covering what it means for a probability to converge to 1. The probability isn't actually necessarily 1, it converges to 1 under certain conditions. e: or 0 or any other probability, for that matter
Yeah. And no, why would I take poison for something that is going to happen? That's just absurd. I could agree to the opposite and take that damn poison if you toss either heads or tails infinity times though.
|
On July 15 2013 23:34 kwizach wrote:Show nested quote +On July 15 2013 17:45 xM(Z wrote:On July 14 2013 22:22 Reason wrote:On July 14 2013 22:07 xM(Z wrote:
"subjective values having "will"" = it's when you give a greater then value to the believes of a determined system in detriment of the believes of another determined system. (the deterministic validation for the judicial system).
"comes from outside events taking place in a deterministic universe." = abstract notion regarding the inner workings of evolution itself. if evolution were to be a software, determinism and nondeterminism would be its 0 and 1. Yeah, I have no idea what you're talking about anymore. your definition Causal determinists believe that there is nothing uncaused or self-caused. every time you use a notion that doesn't follow the deterministic logic of cause and effect, that notion comes from nondeterminism. shit like "greater good" , "common sense" , "value" , "subjectivity" , "objectivity" , "justice" , "singularity" and so on and so forth, do not follow the cause and effect narrative. and, if you'd want to include those notions inside your determinism you'd have to: -at micro level you'd have to prove how did atoms came to have those notions (else you'll have to argue about form being more then the sum of its parts, as i said earlier) -at marco level you'd have to know the cause of the singularity. any concept that allows for either the cause or the effect to be unknown, comes from nondeterminism. What I wrote on the previous page: Show nested quote +On July 14 2013 22:25 kwizach wrote:
xM(Z, you seem unable to understand that the existence of values held by individuals is in no way antithetical to a deterministic universe. I personally do not consider the universe to be only deterministic, simply because of the existence of random phenomena (at the quantum level), but even if it was, there is nothing about the existence of subjectivity and values that would require stepping outside of determinism. You are failing to see the connection between the micro and macro levels. It's not the atoms which "came to have those notions". The elementary blocks, which determinism says behave according to causality, can form larger blocks (for example, cells), which still behave according to the laws of physics. Evolution is the process which explains how we have arrived from elementary blocks to complex organisms. That some of these complex organisms are capable of subjectivity and reflexiveness doesn't change in any way the fact what they are made of, their physical components, behave according to causality.
that is just an assumption at this point but even if you'll get to have your https://en.wikipedia.org/wiki/Theory_of_everything it would still be questionable.
see also https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorem
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
|
|
|
|
|
|
EPT
