Reddit mentions of Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs. 1-36) (3rd Edition)

We're not even sure the constants are constant. It's entirely possible they do change in some complicated relationship on levels too large, too small, too fast or too slow for us to notice 'easily'. I know that dodges your question, but it's one hell of a question and answering it directly would be a marked step forward in our understanding of the universe.

Like chip said, the math is just a 'best fit' solution to the events we observe. If you've got the free time you could crack open this book and try moving things around and see what your new maths describe.

I hadn't even passed algebra when I graduated high school though so if you're in the same boat I was in then this book (specifically the later chapters) might give you a better perspective.

This is what I've been using for classic mechanics and E&M

http://www.amazon.com/Physics-Scientists-Engineers-Strategic-Approach/dp/0321752945

Great book

You're going to get a lot of answers based on preference.

You could start with standard high school texts or introductory college texts but not all of them are very good at illustrating the significance of what they are teaching by themselves. For absolute beginners you might choose a book that starts with an introduction to science then approaches physics as the most fundamental science.

I don't know how much education you've had or what your goals are but here is a list of starting materials that is by no means comprehensive:

• Physics for Realists by Rizzi. Some people don't like Rizzi but he does what other authors fail to attempt: puts physics into context and teaches physics from first principles ala Newton and Aquinas. If anything it helps newcomers think like physicists.
  
  
• Physics for Scientists and Engineers by Knight. This is a typical introductory college text. You can't do wrong by starting with a book like this but since they are targeted towards non-majors as well there isn't as much of an emphasis to learn beyond regurgitating basic equations.
  
  
• Just about anything by Brian Greene. Brian Greene is an established physics professor but he writes a lot of pop science books that are accessible to just about anyone. You'll learn a lot of interesting things about physics but you won't learn how to do physics. You can read something like this for motivation or to quench a thirst but it is hardly representative of what studying or doing physics is actually like.
  
  
• The Feynman Lectures. I haven't read any of these myself but a lot of people like them. If you don't know who Feynman is do a little bit of research on him. He's really good at explaining concepts so a layperson can understand them. There are a good bit of videos of him on youtube. It looks like you can read most of these lectures online so this seems like a good candidate for exploration.