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I'm kind a new to this forum. Been lurking here for a while and got some thought that I'd like to get some advice on. But since I'm new, I better present myself a bit.

I'm a programmer since my youth (age 42 now), and never got a formal degree in anything. Nevertheless, I've always been reading a lot and still doing it, but my focus has changed a lot the latest 4-5 years. Before that, I mostly read IT books about all sorts of stuff in software design, programming, 3D maths for graphics, etc. Today, I have drifted towards reading almost entirely about math & physics. 4-5 years ago, I saw some documentary on string theory and thought that this would be the coolest thing in the world to try to understand... I thought to myself, in my endless naivte, that I would like to understand some of this stuff before i die. :)

I went to amazon and ordered:

http://www.amazon.co.uk/Superstring...=sr_1_4?ie=UTF8&s=books&qid=1224883680&sr=8-4

hahaha, well. I opened the book and read the first page.... o0

Off course, pretty soon I realized that the body of knowledge needed to be able to understand that page is big. But, hey, I have got the rest of my life, so I just began buying the books backwards recursively if you know what i mean... (i love books). First thing was to study QFT, yeah right, then QM & relativity. Relativity made a lot of sense but my understanding of the tools needed (tensors) was void. Linear algebra was next. That quickly made a lot of sense, even though its a pain. I also sidetracked into QM and quickly found out I had to do EM first, wave math, etc. That also spawned an interest in functional analysis etc. Off course I also soon found out that my calculus & PDE's was also hopeless, so I studied that. back to relativity and differential geometry soon pops up, and you are soon led to fluid dynamics etc. That about where i am by now... I've also side tracked into a myriad of other fields (no pun intended) like abstract algebra, noneuclidian geometry, topology, numerical methods, chaos and more.

As you probably have guessed by now, I'm NOT a scientist. When I say I've studied that, I mean I am (still) studying that, in a constant bouncing back and forth between different disciplines and different levels of complexity. This is the way I work. I prefer to look at it all, increase my knowledge of it all, instead of taking it a step at a time. I know also that this is silly if one is thinking about efficiency, but this is a hobby for me and my ADHD is getting in the way of the linear path.

Which brings me to my question. Maybe its silly, but that is the price to pay for the lack of exactness in my approach and this might be something really fundamental and you will shake your heads and all ;)

1) What does linear mean?

I know about the superposition property and homogeneity conditions for a linear thinggy.

When we use the line in the plane (to illustrate homogeneity?), is this just an analogy that shouldn't be taken literally? The reason I'm asking, is that it seems to me that this is relative to the geometry? What is a line? Can a curve on some manifold by considered linear? A geodesic? Doesn't it all depend on the metric? Is it just because the term 'linear' is bound to the usual euclidean xyz geometry in the mind of us all?

Maybe there is a deeper level of knowledge about the linear/nonlinear world. I cannot help but think that this dichotomy must be fundamental. Is there some literature out there that focuses on this? What books should I read to understand the concept of linearity?

Have a nice evening.

/Frederic

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# Concept of linearity?

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