Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum Can we lay nothing to rest?

Finally something I totally agree with.

Yes I understood your logic and agree it is one of many possible answers and it was the one that made sense to you. You were never wrong but you were never explicitly right either.

However as you have obviously now worked out the parameters or definition of the problem you are trying to solve (what we call the maths argument) generally will actually define which of the infinite answers is the one singled out and generally you can not pre-judge it like you did.

As an example if I was plotting a diagonal line thru the complex numbers the next "count" should be the next point 1 unit away on the line and it will be one of two, one you consider forward one you would call backwards. How you decide the direction is also usually defined by the maths argument.

It's actually a very important concept to grasp that the full grid of complex numbers may never if ever be valid answer or inputs.

When I worked out you were treating EVERY complex number as a valid solution it wasn't hard to frame a question where it gave really stupid results to try to get you to see the issue.

That is why we call that complex grid you did your vector maths on a "solution space". There is no guarantee your solution space answer is valid until you map it back thru the maths argument and generally what you hope happens is only one of the answers in the solution space is valid to the argument.

Now you have got that concept sorted and you even understood what a reimann sphere does you can see things a lot clearer. I actually think even with all the antagonism you are at least thinking and seeing the logic and problems clearly.

Now a new caution you are bringing in standard vector maths as a solution to all complex maths. Look at the surface of a reimann sphere it curves in 3D so your vectors curve in 3D and hence you usually switch to polar maths. I am sure you will understand this now.

This all feeds back to my original question to Bill S which is what solution spaces/number system should we be using. Now armed with your clearer understanding you should see the shape of space may ultimately be very important to this question.

I don't have an answer and never did just interesting things to discuss.