Decentralization: Why Good and Bad Schools

[stellarrenegade]

Rationals can do my HW

That's basically what I got out of this thread. This thread is like that Champion video I posted except filled with mathematical equations and exploding graphs instead.

Well, I understand all that about the Internet being the cutting edge, but where does the chaos come in? Everything seems much more streamlined now.

Nevermind, I'm not even gonna try. Just tell me when to buy my ticket to Mars and I'll be there.

[Quinta]

Much clearer. THANKS!

[stellarrenegade]

This is my interpretation of all this chaos:


(along with the pic in my sig)

Tank Girl, Apocalypse with the entire cast: Tank Girl, Sub Girl, Jet Girl and Booga, Tankie's kangaroo boyfriend.

Our beer-guzzling heroine is pregnant and the followers of the Blood God Baal think it's the savior/destroyer of the world, a meteorite hits earth, celebrities die off one by one, and the whole crew escapes to go party on Mars.

Definitely not the best in the series, but hey, it's Tank Girl, and the covers look pretty amazing, even if the story is so-so.

Lost my copy of it in the move, though, dammit. I can't figure out where any of my graphic novels are except for one.

[keirsey]

Well, I understand all that about the Internet being the cutting edge, but where does the chaos come in? Everything seems much more streamlined now.

Chaos: Most emails, Porn sites, internet chain mail, millions of blogs about what people had for breakfast or dinner -- or WHO CARES. It will all be changed and forgotten.

[christina]

How about this, visualize: Euclidean space: R^n is diffeomorphic to Hyperbolic space: H^n, with Fractals (Hausdorff dimensions) in between. Perfect Order R^n at one end, and Perfect Chaos H^n at the other end. Too abstract, oh well, I tried.

How is a Hyperbolic space Perfect Chaos?

Good question!!!?? I think I will have a good answer (articulate answer) in a couple of years. For now, since I don't have the time to give you sufficient answer at the moment, consider the following. First, I was bending the truth, because when I referred to R^n and H^n, where I should have referred to R^infinity (an infinite Hilbert Space) and H^infinity (who knows what this is?) for PERFECT chaos OR order, which is not real. And is of course the SAME (again, diffeomorphic), nothing and everything simultaneous. But ignoring this problematic situation, PERFECT, to almost the same but slightly off -- "almost" PERFECT. Consider Euclidean as being associated to "infinite integers" (e.g., perfectly linear and ordered, and "infinitely independent") whereas Hyperbolic as being associated with "transcendental numbers" (by their inherent structure, non-linear, infinite, and in some sense chaotic, and "infinitely entangled").

Remind me ( I mean inform me) how the word "chaos" is being used here.




Chaos--The opposite of order? perfect disorder (or, that is, 'almost perfect')? That means being able to be specific about what the "order" is exactly and then "reversing" it? "Reversing" order wouldn't necessarily be "disorder" because there are more than one way to "reverse" the order, hence the "hyperbolic space"?***



***I'm using this piece of info from wikipedia:
The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false.

You know what's nice? intense color (see my current avatar).

[christina]

This is probably a lost cause......but has anyone else tried to visualize math as colors or as something in motion?

hmmmmm, I'll use that basic idea of an inverse function ( sorry if this is all wrong...calculus is rather elusive, for me anyways, and please don't say "it's only Calculus, it's so easy" )

I would imagine myself as a speck ("spectating") in (engulfed by) infinite white space and infinite black grid lines and then I would imagine a glass wall and on other side more white space and more black grid lines.


Anyone ever use those etch-a-sketch thingys? On a clean slate, there is one black dot and you controlled it's direction with the two knobs? Meanwhile, the black dot's motion became a line?

Well, in my imaginary land.... god, this is a little embarrassing.....there would be that black dot and a curve would appear.....meanwhile the graph of that function's slope would appear on the other side of the glass wall.

You can see the trail of goo that a snail leaves behind it.....I would watch that little dot moving and see it's trail form behind it. Only after sitting and watching the actual steps 'in motion' did I even begin to see what was being talked about in my text.

[Goodrum]

So we are having different temperaments express their perception of science?

That is wonderful. I see it as beautiful and raw, cyclic, dynamic, rigid, infinite, inflexible and then fluid, sometimes confusing, and "a poetry". Science is a type of poetry. I think it is very beautiful.

Christina I think it would be nice if we were let cut loose in a lab. Just for a day, like wife swap but it could be....temperament passion swap. They could remove the more dangerous stuff, leave us a few recipes and we could improvise as necessary.

I think MKB would like that too.

[christina]

Okay, new topic!


Anyone watch On Golden Pond and eat soup out the can?

[shytiger]

:oops: This is probably a lost cause......but has anyone else tried to visualize math as colors or as something in motion?

hmmmmm, I'll use that basic idea of an inverse function ( sorry if this is all wrong...calculus is rather elusive, for me anyways, and please don't say "it's only Calculus, it's so easy" )

I would imagine myself as a speck ("spectating") in (engulfed by) infinite white space and infinite black grid lines and then I would imagine a glass wall and on other side more white space and more black grid lines.


Anyone ever use those etch-a-sketch thingys? On a clean slate, there is one black dot and you controlled it's direction with the two knobs? Meanwhile, the black dot's motion became a line?

Well, in my imaginary land.... god, this is a little embarrassing.....there would be that black dot and a curve would appear.....meanwhile the graph of that function's slope would appear on the other side of the glass wall.

You can see the trail of goo that a snail leaves behind it.....I would watch that little dot moving and see it's trail form behind it. Only after sitting and watching the actual steps 'in motion' did I even begin to see what was being talked about in my text.

Isaac Newton invented Calculus (independently of Leibniz, although he never admitted as much) with this idea in mind. He called his new mathematics the science of fluxions to indicate that it was to describe things in flux (motion). As David remarks, Newton had to assume the notion of continuous motion, which is fine for most applications. Lee Smolin is hoping Newton was wrong and that the discreteness of spacetime can be measured. I personally think that the universe can have aspects of discreteness and continuity. My guiding principle in all physics research is that every model has a range of validity. Nothing is really "true".

There are books out there that are written specifically for the visual person. I have a book called "Visual Complex Analysis" which is handy for a visual person like me. Look up things like Visual Calculus or Visual Geometry. Shytigress can't stand visualization. "Give my symbols!" she says .

[jwetmore]

Keirsey wrote:

I think Murray is a good read, and I agree with much he has to say, but "differing IQs" does not consider Temperament, in Murray's meaning.

The schools have no sense of the differing IQs of the Temperament, hence very "smart" Artisans are considered "dumb" because their Temperament intelligence is not considered. Teachers don't know how to teach to different Temperaments.

Some kids, like me were ready for abstract algebra, much earlier than it was presented to me. Learning the details of fractions was boring to me, I only need a few examples, not a whole year of the crap. Others, have natural abilities not in concert with "mathematics" -- their natural talents (interest) are in more manipulation of visible objects, such as tools. Temperament matters.

Let me repeat, TEMPERAMENT MATTERS. It probably matters as much or more than IQ and EQ.

This is my chief beef with public schools, and with ideas such as No Child Left Behind. Centralized planning generally leads to one size fits all solutions. The market is more flexible (and chaotic), but is more robust. I don't pretend to have the solutions, but I am sure that unless we allow experimentation, trial and error, and the errors are abandoned, that we will not improve results. We waste enormous potential with our current public school system. Vested interests and top down planning are best at stagnating innovation, and continuing failed policies because they serve narrow, yet powerful interests.

The above does not mean I support anarchy. I do however support experimentation and individual choice. The internet, through sophisticated filtering processes, strongly supports this indivualization. If not for the internet KTT would likely have a smaller following than it does now, and MBTI would have a better chance of remaining dominant, despite its weaknesses compared to KTT.