I'll never forget the first time I grokked trigonometry. I was in high school and my teacher had drawn the unit circle on the blackboard and as theta swept around the circle he plotted the values he measured for the sine, cosine and tangent on separate Cartesian coordinate grids. As the sine waves and graphs of the functions began to reveal themselves as visual graphic shapes, I suddenly understood how these totally unexpected relationships were somehow hidden in the dry definitions and cold equations. It was almost as if triangles had been playing these secret games with themselves since the creation of the universe and I was just discovering them: a cosmic dance formerly hidden to my eyes, which repeated itself over and over again in the physical universe of gravity and electricity, sound and light. Did we invent this, or discover it?
There is a book about mathematics (I've never actually read it) entitled "The Man-Made Universe". What a perceptive title! Did all this always exist, since time began? Or is it a product of man's ingenuity and intellect? Either way, isn't it wonderful that this abstract mental reality seems to have such an intimate connection with the "real world" of physics, and that all this philosophical hand-waving is actually essential for the work of those humorless, dry engineers and their world of concrete measurements and precision nit-picking. And I was getting this in a high school elective while all my friends were taking Business Math.
And after trig comes analytical geometry, and then calculus...
Off Topic » in reply to review
High Strange and Real Analysis.
The whole thread (51 posts)
- Some hints for UFO investigators
- re: Still wondering
- Well put
- Pareidolia
- Distance
- But if you had multiple accurate and trustworthy sightings...
- "Ezekial saw a wheel, way up in the air..."