Gary
GaryVasco
Posts: 3,352 
|
Post by Gary on Nov 26, 2016 23:19:58 GMT
line 3: "we stereographically project onto the tangent plane at the point antipodal to q"
I experience a few moments of confusion reading this. I at first read it to mean the projection should fall at the point antipodal to q. It should be read to project onto the plane that is tangent to the hemisphere at the point antipodal to q, which point is indicated by the black dot in the horizon of the upper half plane.
|
|
|
|
Post by Admin on Nov 27, 2016 8:12:54 GMT
Gary
Yes, that is a confusing phrase. Once you understand its two or three different meanings from a linguistic point of view, then its fairly easy to decide, with the aid of 41, which one Needham intends.
When I am re-reading some of my own documents, before I "publish" them, I often find ambiguities of this type. Sometimes, to make things totally unambiguous, my explanations can become too wordy, and then I cut them back again at the risk of leaving in some ambiguities which I hope the reader will be able to resolve without too much trouble.
The effort involved in trying to make the meaning of written work as clear to the reader as possible often pays dividends by revealing to the writer some of the flaws in the argument.
It's clearly a huge advantage to have someone else read what you have written and give you some feedback.
Vasco
PS Funnily enough, I find the phrase just after the one you quote, hard to understand - maybe you have an explanation:
"...antipodal to q - actually, any plane tangent to this one would do equally well."
Can a plane be tangent to another plane? Does he perhaps mean parallel?
|
|
Gary
GaryVasco
Posts: 3,352
|
Post by Gary on Nov 27, 2016 21:03:14 GMT
Gary Yes, that is a confusing phrase. Once you understand its two or three different meanings from a linguistic point of view, then its fairly easy to decide, with the aid of 41, which one Needham intends. When I am re-reading some of my own documents, before I "publish" them, I often find ambiguities of this type. Sometimes, to make things totally unambiguous, my explanations can become too wordy, and then I cut them back again at the risk of leaving in some ambiguities which I hope the reader will be able to resolve without too much trouble. The effort involved in trying to make the meaning of written work as clear to the reader as possible often pays dividends by revealing to the writer some of the flaws in the argument. It's clearly a huge advantage to have someone else read what you have written and give you some feedback. Vasco PS Funnily enough, I find the phrase just after the one you quote, hard to understand - maybe you have an explanation: "...antipodal to q - actually, any plane tangent to this one would do equally well." Can a plane be tangent to another plane? Does he perhaps mean parallel? Vasco, I missed that one. "Parallel" would work. In fact, for some unknown reason, that is how I read it. He might also mean "any vertical plane tangent to the hemisphere at the equator", but that would not necessarily work with the given semicircles. Gary |
|
