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How big is infinity?
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Hugh
No if a Doc failed all it means is that he or she wasn't able to complete tasks that are mandatory for helping people.
You're being a ridiculous crap stirrer at this point, as usual, and I'm out of this.......
Nice. What a great example of how one reacts to a brief challenge to their basic misconceptions. Perhaps stirring a little crap is exactly whats needed so that lifeline misconceptions are finally questioned.
 

Stranger

How big is infinity?
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How is it imperfect? Give me one example of how Maths is imperfect. Just one.

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It can't prove itself. It can't even prove all supposed truths. Therefore the system is incomplete, and hence, anything can be proven using this system.
 

Stranger

How big is infinity?
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Correct me if I'm wrong, but aren't those theorems more about you not being able to prove certain things rather than being able to prove that 2=3 or something similar? I've seen equations that would "prove" that but they are fallacies that require incorrect math.
What the theorem found was that by using the arithmetic of whole numbers, one cannot demonstrate the consistency of such a system within itself, in other words, it is undecidable. Hence, one can't use a systems own workings to determine if it is consistent or not. Even if the system is consistent, one must reach outside the system to prove it, but the external system must be provable in order to have confidence in the primary system.

The first incompleteness theorem showed that some perfectly well-formed arithmetical statements could never be proved true or false. Worse, it showed that some arithmetical truths could never be proved true. More precisely, for every axiomatic system designed to capture arithmetic, there will be arithmetic truths which cannot be derived from its axioms, even if we supplement the original set of axioms with an infinity of additional axioms. This shattered the assumption that every mathematical truth could eventually be proved true, and every falsehood disproved, if only enough time and ingenuity were spent on them.

The second incompleteness theorem showed that axiomatic systems of arithmetic could only be proved consistent by other systems. This made the proof conditional on the consistency of the second system, which in turn could only be validated by a third, and so on. No consistency proof for arithmetic could be final, which meant that our confidence in arithmetic could never be perfect.

In quick succession, Gödel deprived arithmetic of its hope of completeness and its certainty of consistency. These were devastating blows to the concepts of logic and mathematics that prevailed in 1931 when Gödel published his proofs at age 25.

http://www.earlham.edu/~peters/writing/godel.htm
 

kurtfaulk

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It can't prove itself. It can't even prove all supposed truths. Therefore the system is incomplete, and hence, anything can be proven using this system.

I don't even know what the hell you're talking about. You said maths is imperfect, it's not up to maths prove itself. Just give one example of how it is imperfect.

.
 

Stranger

How big is infinity?
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Nobody, you're just intelligent in different aspects. Assuming that you can recall and perform said tasks/information correctly. The problem is when people who aren't intelligent in certain areas assume they are.
Define "correctly". Is your correctly the same as my correctly?
 

Stranger

How big is infinity?
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I don't even know what the hell you're talking about. You said maths is imperfect, it's not up to maths prove itself. Just give one example of how it is imperfect.

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Well, if it can't prove all truths, then wouldn't you say it's imperfect? If I have to use another (external) system to prove all proofs, then why should I rely on the primary system? Bottom line, it is not a perfect system, nor is it a complete system. It has significant limits, and is not absolute as we've been taught.

The therem is important and relevant, namely, because all theories and systems possess holes (ie. are incomplete and therefore inconsistent). Hence, whatever theories are the most appealing "win" and gain acceptance in the public mind.

Here's a video clip from BBC's Dangerous Knowledge
Embedded media from this media site is no longer available

Embedded media from this media site is no longer available
 
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bluecoconuts

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Define "correctly". Is your correctly the same as my correctly?

Correct is correct. It is correct to say the largest known galaxy in our universe is IC1011. It's like shooting, you either hit the bullseye or you don't. If you miss you can't say "well I hit in my book" just like if you say "well in my book the Milky Way is the biggest". Those are incorrect. There can be several ways to accomplish something, and in some cases several right answers, but correct is correct. If you are correct and can consistently repeat those results (rule out being lucky once) then I'd say you've demonstrated at least some level of intelligence on said subject matter.

Well, if it can't prove all truths, then wouldn't you say it's imperfect? If I have to use another (external) system to prove all proofs, then why should I rely on the primary system? Bottom line, it is not a perfect system, nor is it a complete system. It has significant limits, and is not absolute as we've been taught.

The therem is important and relevant, namely, because all theories and systems possess holes (ie. are incomplete and therefore inconsistent). Hence, whatever theories are the most appealing "win" and gain acceptance in the public mind.

Here's a video clip from BBC's Dangerous Knowledge
Embedded media from this media site is no longer available

I wasn't speaking about the previous argument, I was more curious if you had a formula that said 2=3 and had no fallacies.
 

SteveBrown

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define intelligent. seriously, can you?
The ability to learn. That is my closest guest; though I do believe there are certain "IQ's" that live outside of this definition---of them being musicians like Keith Richards who doesn't learn, but can re-apply the same thing over and over and get a cool and differently discernible result with a repititve melody line from song to song....I love Keith, by the way. He can be a bit of wordsmith, too. Can Keith learn--I don't know...so, maybe some types of creativity are not so testable. Because if you don't like "Happy" or "Beast of burden" you don't understand the genius ;)
 

SteveBrown

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Um... I call bullcrap. This is sadly a racial mantra based on a line from a sitcom. That hasn't kept it from becoming fact on the internet though. However, if you can actually find the test that the question shows up in, I'll kindly retract this. Good luck.
I worked/tutored a lot of inner city kids (Cheecago);and they are not "trained" on the south side by the parents; the home training is more important than the schooling. IF a kid is not 'trained' before, and during school by parents, the schooling doesn't work so good. I love the south side of chicago, and dig those kids, but everyone who lives there knows these kids don't receive training. Therefore, VERY few of these kids can from the south side can take tests written by a north side professor. YOu have to 'live' this, like I did, to really feel how deficient the training of the south side kids is...you have to enter a few dozen homes and see what there parents are teaching them...
 

SteveBrown

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I got a 50. I'm not trying to brag or anything. I did go to the school for the gifted and I am a doctor. But those questions are ridiculously easy. I weep for those who can't get above a 10
How do I get to be gifted---I want that; I am a lead guitarist, but I don't wanna brag cause I can jam out the Stones and talk a coherent conversation at the same time (Broadcast news)
 

SteveBrown

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Okay, that's a good one. So, say I have different ability to gain and apply different tasks than you do. Who decides whose ability is "intelligent" and whose ability is not intelligent? Or, who decides which tasks completed quickly determine intelligence?
I think QB's, linebackers, safeties and WR's are really better off if they are smart. Tavon is smart enough to succeed, I believe. Brian Quick has been slower in picking up the offense; I bet if he had Sam's intelligence, he would be doing well already; If i had sam's intelligence, I might be a lot better off!

O lineman are better off if they are smart; but physical ability and muscle memory development can do wonders, too. Incognito got a 31 if I remember (or at least a 28). He played center with ease--and did well; so, he is probably football smart....oops I brought Cogs in to this...sorry.
 

Stranger

How big is infinity?
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Hugh
Correct is correct. It is correct to say the largest known galaxy in our universe is IC1011. It's like shooting, you either hit the bullseye or you don't. If you miss you can't say "well I hit in my book" just like if you say "well in my book the Milky Way is the biggest". Those are incorrect. There can be several ways to accomplish something, and in some cases several right answers, but correct is correct. If you are correct and can consistently repeat those results (rule out being lucky once) then I'd say you've demonstrated at least some level of intelligence on said subject matter.
So, individual human observation plays no role. There is objective fact outside the human experience, and either we all see it the same way or we do not?. Is that your argument?

Let me share with you an alternative view, one espoused by the late head of the University of Illinois Bio-Computing Lab...



@2:10

Interviewer: "But science, and your own resarch... those are not just inventions or good stories? Surely, they're based on mathematics, on numbers, on provability, on indisputable scientific data?"

Heinz: "Well, yes, but these days there is already so much data that it is no longer possible to include all the different data in your 'story'. And then artificial data is invented. For example, 'particles'. .. Then 'particles' are invented that do whatever it is we don't understand. So, in my opinion particles are always the solutions to problems that we can't solve any other way. That is, they are inventions that help to explain certain problems. Those are particles....

Let's say there is a hole in my theory, one I can't gloss over. So, what I do it, I just say: Look, here are some new particles, that are either green, yellow or... I don't know what.... They replace the hole in my theory.

So, I maintain that each particle we read about in today's physics is the answer to a questoin that we can't answer.


@3:30

Interviewer: "How can we let a world-wide networked system of machine grow, more or less into infinity, if it is based on theories that apparently have holes or are only 'good stories', I mean on such shaky foundations? Isn't that dangerous?"

Heinz: "Well, in this world-wide, function system of machines all theories are correct. And of course, that's what people want.

Any why are they correct? Because they can all be deduced from other theories and 'stories'....."

Interviewer: "But what will it lead to? How does it go on?"

Heinz: "It goes on deducing indefinitely. "

Interviewer: "But there have to be limits somewhere?"

Heinz: "No, not at all, that's the good thing about it. You can go on forever."

Interviewer: "In logic. Yes, precisely. But in reality?"

Heinz: "Where is reality? Can you show it to me?"

I wasn't speaking about the previous argument, I was more curious if you had a formula that said 2=3 and had no fallacies.
No, this was merely a simple way to make my point. There is no formula that I know of to show this. But, the logical proof does exist to show maths inconsistency.
 
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Stranger

How big is infinity?
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The ability to learn. That is my closest guest; though I do believe there are certain "IQ's" that live outside of this definition---of them being musicians like Keith Richards who doesn't learn, but can re-apply the same thing over and over and get a cool and differently discernible result with a repititve melody line from song to song....I love Keith, by the way. He can be a bit of wordsmith, too. Can Keith learn--I don't know...so, maybe some types of creativity are not so testable. Because if you don't like "Happy" or "Beast of burden" you don't understand the genius ;)
So, say I am able to more easily learn philosophy, meaning I can read a book written by a philospher and regurgitate it and it's subsequent meanings quickly after 1-read. Then, let's say you on the other hand can read a book about music and musical concepts and regurgiate its deeper meaning quickly after 1-read. Neither of us can read what the other is reading and understand it very well, as I certainly have never understood music and I certainly don't know why "Happy" is genius. So, who is "more intelligent", or who has the higher IQ?

This is precisely why I don't like the Wonderlick test, nor any standardized testing scheme.
 

Stranger

How big is infinity?
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I worked/tutored a lot of inner city kids (Cheecago);and they are not "trained" on the south side by the parents; the home training is more important than the schooling. IF a kid is not 'trained' before, and during school by parents, the schooling doesn't work so good. I love the south side of chicago, and dig those kids, but everyone who lives there knows these kids don't receive training. Therefore, VERY few of these kids can from the south side can take tests written by a north side professor. YOu have to 'live' this, like I did, to really feel how deficient the training of the south side kids is...you have to enter a few dozen homes and see what there parents are teaching them...
So, what are those kids good at? What are things that they understand early, well before their north side peers? Can you think of anything that you'd be willing to share?
 

kurtfaulk

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Well, if it can't prove all truths, then wouldn't you say it's imperfect? If I have to use another (external) system to prove all proofs, then why should I rely on the primary system? Bottom line, it is not a perfect system, nor is it a complete system. It has significant limits, and is not absolute as we've been taught.

The therem is important and relevant, namely, because all theories and systems possess holes (ie. are incomplete and therefore inconsistent). Hence, whatever theories are the most appealing "win" and gain acceptance in the public mind.

we're going around in circles here.

i will give you a few basic maths equations. you tell me if they are correct or incorrect and why.

4 + 5 = 9
10 - 7 = 3
4 x 3 = 12
8 / 2 = 4

the most basic of maths equations that any educated person should know. bearing in mind this is the system that was created by someone a long time ago and the whole world uses it till this day. just like all the languages invented in the world that people use every day and we are now.

.
 

Stranger

How big is infinity?
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we're going around in circles here.

i will give you a few basic maths equations. you tell me if they are correct or incorrect and why.

4 + 5 = 9
10 - 7 = 3
4 x 3 = 12
8 / 2 = 4

the most basic of maths equations that any educated person should know. bearing in mind this is the system that was created by someone a long time ago and the whole world uses it till this day. just like all the languages invented in the world that people use every day and we are now.

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Math is correct, and these examples are correct, because you and I agree that they are correct. That's all. It's an agreement between you and I because we both went thru similar indoctrination growing up.

Math is a man-made system, a set of tools, that we agree on in terms of how it works. That's all it is. See the video I posted a few posts ago.
 

kurtfaulk

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Math is correct, and these examples are correct, because you and I agree that they are correct. That's all. It's an agreement between you and I because we both went thru similar indoctrination growing up.

Math is a man-made system, a set of tools, that we agree on in terms of how it works. That's all it is. See the video I posted a few posts ago.

it was taking too long to buffer for me. but i agree with everything you've said in that post. this is the system the whole world knows and it works. i'm not going to question it because it works so well and i use it everyday in my line of work. i just don't see the point in trying to debunk it.

.
 

Stranger

How big is infinity?
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it was taking too long to buffer for me. but i agree with everything you've said in that post. this is the system the whole world knows and it works. i'm not going to question it because it works so well and i use it everyday in my line of work. i just don't see the point in trying to debunk it.

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I'd say I'm trying to communicate its limits, not debunk it. We've been taught that math is absolute, just as we've been taught that examinations and methods of measuring intelligence are absolute. And my point is to question this absoluteness, because these man-made systems are limited and fallible.

Here's a longer version of the video on Dangerous Knowledge (which I posted previously). Watch the last couple of minutes where they discuss humanity's need to believe in absolute certainty, and systems that supposedly give us such certainty, when in actuality there is none.

 

Mojo Ram

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Evil Spock does not approve of this thread.
th
 

jap

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How is it imperfect? Give me one example of how Maths is imperfect. Just one.

.

Consider this classic example illustrating the limitations of binary logic (or two-valued logic or mathematical logic or whatever). A person makes the statement, "I always lie." If true, the person was lying when they made the statement, and the statement is a contradiction. Yet, if the statement is true, then the person is also contradicting him|herself. This is known as the Liar's Paradox. It illustrates that simple logical systems with only a few values (true|false, yes|no, 1|0, in|out, etc.) to establish truth are not rich enough to handle the complexities of real life that allows seeming paradoxes like the above.

Another logical oversimplification and one more germane to sports is the failure of the transitive property of inequality when applied to real life. Team A beats Team B; Team B beats Team C; therefore, Team A necessarily will beat Team C. Of course, we know there is no guarantee there for the same reason as above. Simple systems like most mathematical systems are not rich enough to analyze the complexities of real life where there are so many variables involved.

Other difficulties involve things like division by zero. The standard answer of division of a non-zero term by zero being undefined is really unsatisfactory. If we divide the number 12 (the dividend) by 4 (divisor), it is easy to regard this is computing that it would take 3 (quotient)
groups of 4 to comprise the number 12. So division can be viewed as deciding how many groups (quotient) of the divisor are needed to make up the dividend. However, if one divides a number, say 5, by zero, the standard answer of undefined or positive infinity is unsatisfactory since it is fairly obvious that one can never find any groups of zero that will make up the desired result of 5.

Don't get me started on the philosophical
difficulties with infinity.