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#11
08-12-2005, 08:47 AM
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Re: Del and the Laplacian
Bruce, Good Morning and Congrats.
[ QUOTE ] , or the curl (vector) when we take the cross product of del with a vector. [/ QUOTE ] If you don't call the cross product a mathematical operation, all I can say is some people say tomato. And yes, the dot product always results in a scalar but the cross product always results in a vector. That post was limited to the topic of vectors. [ QUOTE ] which gives a sum of second partial derivatives in Cartesian coordinates. [/ QUOTE ] I take issue with this in that Vector math is not restricted to any specific coordinate system; Cartesian (x, y,z), Cylindrical (r, theta, z) or Spherical (R, theta, phi). I wish that it were (it would have saved months in my life) lol. [ QUOTE ] String theory had 10 (9 spatial and 1 time), membrane theory has 10 or 11. Bosonic string theory has 26. [/ QUOTE ] These are all divergences in String Theory which shows that the subject matter is a "work in progress". I was just trying to point out as simply as possible how reasonable it is to think in multiple and different dimensions because Combinatorial math may not answer all our questions and we are subject to these limitations.. 
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#12
08-12-2005, 09:58 AM
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Re: Del and the Laplacian
[ QUOTE ]
Congrats [/ QUOTE ] For? [ QUOTE ] If you don't call the cross product a mathematical operation, all I can say is some people say tomato. [/ QUOTE ] Huh? Where did I say anything about it not being a mathematical operation? Of course it is. [ QUOTE ] And yes, the dot product always results in a scalar but the cross product always results in a vector. [/ QUOTE ] The Laplacian is not a cross product. The Laplacian is the dot product of del with the gradient. The Laplacian operates on functions not vectors, and it gives a scalar, not a vector. [ QUOTE ] That post was limited to the topic of vectors. [/ QUOTE ] Then why bring up the Laplacian? [ QUOTE ] [ QUOTE ] which gives a sum of second partial derivatives in Cartesian coordinates. [/ QUOTE ] I take issue with this in that Vector math is not restricted to any specific coordinate system; Cartesian (x, y,z), Cylindrical (r, theta, z) or Spherical (R, theta, phi). I wish that it were (it would have saved months in my life) lol. [/ QUOTE ] I said that it only gives a sum of second partial derivatives in Cartesian coordinates. In cylindrical coordinates, there is a first partial with respect to r multiplied by 1/r, and the second derivative with respect to theta is multiplied by 1/r^2. In spherical coordinates, there are factors of R^2 and sin(theta) which are multiplied by the first derivative with respect to R and theta respectively, before taking another first derivative. Also, the second derivative with respect to phi^2 is multiplied by 1/sin^2(theta), the theta term is multiplied by 1/sin(theta), and all terms are multiplied by 1/R^2. [ QUOTE ] I was just trying to point out as simply as possible how reasonable it is to think in multiple and different dimensions because Combinatorial math may not answer all our questions and we are subject to these limitations.. [/ QUOTE ] What kind of poker problem do you think can't be solved with combinatatorial math that can be solved with vector math?
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#13
08-13-2005, 07:06 PM
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Re: Del and the Laplacian
BruceZ,
You crack me up, I love reading your stuff even though I don't have a clue what your talking about most of the time, I keep hoping something will click someday... [img]/images/graemlins/grin.gif[/img] You really like mixing it up with these guys and I think that's what makes it fun to read Now as I have not contributed anything of value to this discussion I shall dismiss my self [img]/images/graemlins/smile.gif[/img] One Street at a Time wdbaker Denver, Co
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