Re: Fundamental Frequency and String Relation

Posted by rtharbaugh on September 16, 2003 at 14:30:41:

In Reply to: Fundamental Frequency and String Relation posted by sol on September 16, 2003 at 08:13:05:

Sol

Thanks for the interesting links. You gave the Patricia link once before, and I commented that it takes three points to describe a circle, but only two points are shown in the diagram. I see now that in the Poincarre upper half plane, only two points are needed to make a circle, which is an effect of the half plane being a non-euclidian space.

I have to wonder if these non-euclidian metrics are confusing us. Well, me, anyway. After all, we must return eventually to real world experiments, even though the math worlds are very interesting, and in the world as we know it, three points are required for a circle. I guess it is my poor math skills that required me to stick to thinking of stacking spheres as a model for higher dimensionalities, rather than going into the math of higher dimensions, where many elegant solutions have been found that have no visual constructive metaphore. The numbers come out right, so something must be there, but I am child-like enough to want to stick to my marbles and clay. Solid geometry is my experimental basis.

I read your comment on the difficulty of using the slash mark to indicate "over", as we do in division. I get around this problem by using negative exponents, which can be difficult to read if you are not used to them but does seem to me to solve the slash problem. For example, we may write x/y, meaning x divided by (or over) y, but in exponential notation that is the same as multiplying x by the inverse of y, 1/y, which is also written y^-1. So 1/y^2 can be written y^-2 and so on. Then x/y is written xy^-1. When you wish to indicate that the product xy is to be raised to -1, you can use parenthesis, as (xy)^-1, which in slash notation would be 1/(xy). Without parenthesis, the exponent is attached only to the variable immediately preceding it.

Exponential notation is very useful when trying to deal with extremely large and extremely small numbers, as we seem always to be doing in string theory.

Thanks,

Richard


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