Welcome, Guest. Please login or register.

Login with username, password and session length

Tradition in mathematics

Tradition in mathematics
March 04, 2010, 03:41:17 PM
Quote
In probability theory, the central limit theorem (CLT) states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed (Rice 1995).

http://en.wikipedia.org/wiki/Central_limit_theorem

Among other things, this means that the more "diverse" we try to be the more the diverse will become the norm. You cannot force diversity. It emerges from within.

Even more, it tells us that no matter how independent, unique, weird and wild we try to be, we fit somewhere on the spectrum -- there is no way to escape the spectrum itself.

In short, a large defecation on free will. :)

Re: Tradition in mathematics
March 04, 2010, 04:18:48 PM
Very interesting.

So, Nothingness is something that determines us as beings after all.


Re: Tradition in mathematics
March 04, 2010, 05:47:27 PM
If you want to play "civilisation" the aim of the game is to normalise your own ideas within the system. Drag that hump over to your own position. Then ideas far away from yours will become rarer and rarer and what was once normal will become extreme. Even the extreme, then, are brainwashed. This is why the general population don't even notice the possibility of propaganda in their own society. Thanks for this, very insightful; statistics is a subject I don't pay enough attention to.

E

Re: Tradition in mathematics
March 04, 2010, 06:01:29 PM
Among other things, this means that the more "diverse" we try to be the more the diverse will become the norm. You cannot force diversity. It emerges from within.

In the advocation of social utopias, diversity usually isn't a 'permanent revolution' type of deal, as no thought is wasted on its consequences. I'm pretty sure it can be forced, though, bypassing the CLT short-term; like fucking up an ecosystem.

Re: Tradition in mathematics
March 05, 2010, 01:51:12 AM
I don't see how CLT implies that all. It just shows that the mean of a large number of means (ie: mean of class 2009 is 28, mean of 2008, is 26, etc etc, total mean of 27), will be normally distributed around the true mean (27).

It's still possible to exist as an outlier (diverse/extreme) in a normal distribution.

Re: Tradition in mathematics
March 05, 2010, 06:24:35 PM
Quote
The central limit theorem states that as the sample size n increases, the distribution of the sample average of these random variables approaches the normal distribution.

It's not too far an imaginative stretch surely? We're meta-applying statistics; I don't see the harm in this. If a mathematical idea can trigger off an interesting thought process one would never of otherwise had, then I welcome those thoughts gladly.

Re: Tradition in mathematics
March 05, 2010, 08:47:06 PM
I just don't understand the application is all. It's like if someone said to me "You're a part of humanity", that wouldn't bother me, because I obviously fit into the category, but have differing aspects from the norm. There's no amount of determinism in that statement.

Re: Tradition in mathematics
March 05, 2010, 09:12:05 PM
I welcome the interesting though process as well, but human beings are not numbers, and the "norm" exists only theoretically.  We cannot attach quantitative value to a human being in regard to personality, etc.

The main problem with 'equality' is that there is nothing to equate.  Except, as Stars Down to Earth noted, that we are all human.  Comparing theory to reality in cases such as this forces us to see reality in such a way, rather than having found it this way in the first place.

Re: Tradition in mathematics
March 05, 2010, 11:06:04 PM
I welcome the interesting though process as well, but human beings are not numbers, and the "norm" exists only theoretically.  We cannot attach quantitative value to a human being in regard to personality, etc.

Why not? I'll use the CLT as literally as possible, and see what you think of this method of "numbering" a human:

Respect that all things lie on a spectrum; nature works with analogues. Let's say we're looking for the average man. So we take the many different variables of a male human being (how happy, angry, tall, intelligent, etc); quantify where each man lies on that spectrum (even if it is just a big questionnaire asking the person where they feel they fit on that spectrum on a scale of 1 to 10), take the mean of each of these variables. That gives us the current average man. Then we do this every 4 years or so and we'll eventually be able to use the CLT to approximate what the average man is in general (assuming the variable are reasonably enough defined). Of course this has imperfections, but it is applied science after all.


Comparing theory to reality in cases such as this forces us to see reality in such a way, rather than having found it this way in the first place.

This is a good point and perhaps I have been a bit too quick to theorise. One has to be very wary of this, but I still enjoy the discussion and can't see that I'm too far off the mark in my first post.

Re: Tradition in mathematics
March 06, 2010, 09:09:21 AM
Using CLT in this context does not sit well with me. The only thing that changes is the variance/standard deviation in Conservationists case. Increasing the number of significantly different will not change the mean, unless the data is skewed. If the data is skewed, that means the significantly different data were tending toward a value other than the mean, which is a "trend" and not "diversity". Diversity will only increase the variance. See: "directional selection" and "stabilizing selection".
Even more, it tells us that no matter how independent, unique, weird and wild we try to be, we fit somewhere on the spectrum -- there is no way to escape the spectrum itself.
Any quantifiable information will tend toward a perfect bell curve with an infinite sample size. . . I don't understand the what is meant in the quote. I dislike when I see math and physics related to an entirely irrelevant subject. Math and science are meant to represent the physical universe: all concepts are reduced to their fundamentals, so weasel words do not exist, which is contrary to philosophic discussion. I don't understand why there aren't more people in applied science on this forum -- there would be less arguments about trivial matters like this topic. I believe that philosophy (metaphysics), math, and science try to arrive at the same point: representation of the physical universe. My personal preference is math and science over philosophy, so I will stick to arguing with what I know. Besides, metaphysics is rather obsolete.

Re: Tradition in mathematics
March 06, 2010, 09:04:16 PM
I dislike when I see math and physics related to an entirely irrelevant subject. Math and science are meant to represent the physical universe: all concepts are reduced to their fundamentals, so weasel words do not exist, which is contrary to philosophic discussion. I don't understand why there aren't more people in applied science on this forum -- there would be less arguments about trivial matters like this topic. I believe that philosophy (metaphysics), math, and science try to arrive at the same point: representation of the physical universe. My personal preference is math and science over philosophy, so I will stick to arguing with what I know. Besides, metaphysics is rather obsolete.
I'm studying pure mathematics myself; when you're surrounded by it daily it's inavoidable to start thinking in terms of it and applying it to everyday life or noticing how "this reminds me of this theorem" or whatever. It should, however, be regarded mainly as a bit of intellectual fun unless you can really work at it enough to be able to prove it which, by the way, I don't see as unfeasible, just an incredible challenge.
In my opinion the ugliest side of mathematics is it's application to the world by humans; mathematics is an entirely irrelevant subject to Physics and yet it has many, many uses there. I have found that there is a startling difference between a mathematician's mind and a physicist's mind.

Re: Tradition in mathematics
March 09, 2010, 09:20:44 PM