Comments on: Reddit discussion considered productive http://dayvancowboy.org/2006/12/reddit-discussion-considered-productive/ not about meaning, but land surveying and cartography Sat, 11 Oct 2008 05:32:25 +0000 http://wordpress.org/?v=2.6 By: Kisakookoo http://dayvancowboy.org/2006/12/reddit-discussion-considered-productive/#comment-361 Kisakookoo Wed, 24 Jan 2007 05:16:30 +0000 http://syntaxfree.wordpress.com/2006/12/13/reddit-discussion-considered-productive/#comment-361 <p>Hi! Why I can't fill my info in profile? Can somebody help me? My login is Kisakookoo!</p> Hi! Why I can’t fill my info in profile? Can somebody help me? My login is Kisakookoo!

]]> By: dr. k http://dayvancowboy.org/2006/12/reddit-discussion-considered-productive/#comment-360 dr. k Fri, 19 Jan 2007 03:54:46 +0000 http://syntaxfree.wordpress.com/2006/12/13/reddit-discussion-considered-productive/#comment-360 <p>I mean, let's say you have f(x) = x^3</p> <p>Integral from (-a) to a of x^3 is 0. But the <em>area</em> is 2*integral of 0 to a of x^3.</p> <p>See?</p> I mean, let’s say you have f(x) = x^3

Integral from (-a) to a of x^3 is 0. But the area is 2*integral of 0 to a of x^3.

See?

]]> By: Ben Franksen http://dayvancowboy.org/2006/12/reddit-discussion-considered-productive/#comment-359 Ben Franksen Sat, 23 Dec 2006 22:59:58 +0000 http://syntaxfree.wordpress.com/2006/12/13/reddit-discussion-considered-productive/#comment-359 <p>You write: "Moreover, this pair of analogies [derivative-as-angle, integral-as-area] doesn’t yield the basic result of the field (the fundamental theorem of calculus), and working directly with them forever means losing out big time..."</p> <p>Derivative-as-angle is a bad idea to start with. It doesn't even generalize properly to a two-dimensional domain. It should have long ago been completely replaced by the much more general (and still easy to understand) local-approximation-by-a-linear-function.</p> <p>However, integral-as-area generalizes quite well, even to the most abstract setting (measurable function on a measure space). What doesn't generalize is one concrete and very simple-minded method of /calculating/ the integral (the so-called 'Riemann-Integral').</p> You write: “Moreover, this pair of analogies [derivative-as-angle, integral-as-area] doesn’t yield the basic result of the field (the fundamental theorem of calculus), and working directly with them forever means losing out big time…”

Derivative-as-angle is a bad idea to start with. It doesn’t even generalize properly to a two-dimensional domain. It should have long ago been completely replaced by the much more general (and still easy to understand) local-approximation-by-a-linear-function.

However, integral-as-area generalizes quite well, even to the most abstract setting (measurable function on a measure space). What doesn’t generalize is one concrete and very simple-minded method of /calculating/ the integral (the so-called ‘Riemann-Integral’).

]]> By: Julian Morrison http://dayvancowboy.org/2006/12/reddit-discussion-considered-productive/#comment-358 Julian Morrison Thu, 14 Dec 2006 16:40:06 +0000 http://syntaxfree.wordpress.com/2006/12/13/reddit-discussion-considered-productive/#comment-358 <p>"interact" is your friend.</p> “interact” is your friend.

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