Tuesday, August 09, 2005

Imagination is more important than knowledge.

“Imagination is more important than knowledge”.
Albert Einstein.

The equation x*x+1=0 has no real solution, but it has a (two) complex solution(s). You must be able to abstract from the real line to understand that. The Rieman integral over a point (zero length) is zero, nevertheless the Dirac Delta function, a distribution, has all its mass in origo, so the integral over that point equals one. Again you have to abstract and it is easy if you think of a triangle, with … please help med Professor GoogleBot, what is the English word

Search term: “Area of a triangle”

First hit: http://www.aaamath.com/B/geo78_x6.htm

Of course it is base. Thank you professor Googlebot, I have used you for a long time as a dictionary, and you are faster than my “The Concise Oxford English Dictionary.” I do not use an online dictionary, since you are on my toolbar, and you are fast enough for me. Neither do I know of a good free Norwegian / English and have no time to search for one, since I am writing now.

So in order to imagine a function with an integral (area) = 1, you have to take a triangle with base 2/n and height n and then the are = ((2/n)*n)/2 = 1. And when n goes to infinity, the base collapses to a point, a Dirac pulse, that is “so infinite” that it’s integral in origo equals 1.

Kjell Bleivik


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