Neighbor posted Jan 31, 2014 12:07 PM (http://mathforum.org/kb/message.jspa?messageID=9376173): > > > But if you really want to learn math, you need to > at > > least get grounded in the ways that mathematicians > > approach these sorts of problems, even if later you > > want to poke fun at them. Your sort of free-form > > thinking is fun, but its not really math. > > > > Cheers, > > Joe N > > If a beginner starts to learn math, the first > concepts he comes upon are very likely points and > lines. How should we explain to him these? (of > course, not only giving the definition, but also > explaining to him the why of this by means of > rational arguments) > That is to say, telling him In what way he should > approach these sorts of problems. > What is a mathematician? ================ A: "A mathematician is someone whose field of study is mathematics"
B: Only partly in jest, a mathematician has been defined as "a blind man in a dark room looking for a black cat which isn't there".
Both definitions are correct. (And the "black cat that isn't there" is very much 'there' indeed).
Thus it turns out, dear Neighbor, that - in the final analysis - you will have to decide for yourself precisely what it is you need to learn in respect of your 'apparently simple' "question about straight lines" and how you will go about learning whatever it is that you may wish to learn. Check out, for instance, my post dt. Jan 29, 2014 5:24 PM (http://mathforum.org/kb/message.jspa?messageID=9374259), for information about some 'system tools' that could help you learn how to do just what you need, get needed answers to your 'simple' question. The 'answers' will have to come, finally, from your mind.
One difficulty or foncusion that you may be encountering at this point probably arises from the fact that your 'apparently simple' original "question about straight lines" has tuned out to be not so simple at all! In part, this has arisen because each response thus far actually been articulated in the terms of what the responder has seen in your 'simple' question (or wished to understand by it) - and this may not quite correspond to what you might have needed or wanted to learn.
For instance, Joe Niederberger (JN) in his post dt. Jan 30, 2014 9:15 PM (http://mathforum.org/kb/message.jspa?messageID=9374945) has related your apparently 'simple question' to issues involved in General Relativity, Godel Universe(s), (possibly also to Quantum Mechanics, entangled photons, etc), the philosophy of science [scientific discovery], and so on. I've looked through the paper JN has suggested ("Time and Causation in Gödel's Universe" with some care, though without studying it using the modeling tools I recommend: it seems, on my superficial look at it, to be very sound). Once upon a time, these were issues I had very keen interest to investigate in depth and, if possible, to unravel, understand and study myself. From your posts here thus far, I believe that these were NOT issues you were asking about in your 'simple' "question about straight lines" - but then that is only my impression and possibly JN is correct in his understanding about just what it is you m! ay want to learn about straight lines and points, etc.
Anyway, it is up to you to decide precisely what it is you need to understand about straight lines, the infinite number of points 'in' those straight lines, etc, etc: as should be clear by now, this is a question that could involve years and years of quite intense and sometimes quite difficult learning. The 'systems aid' to problem solving and decision making that I've suggested, 'The One Page Management System' (OPMS), may be of some benefit in this respect, to help you decide just how far you may wish to pursue your investigations into "straight lines, the points in/on them", etc, etc.