I decided to write this post because I had a brain blast. I started reading a chapter about contour maps and level curves. It all makes perfect sense! I had a series of little brain bombs, and then suddenly, a nuclear explosion appeared.
- Why we have multi-variable functions
- What do these look like
- What is a contour line/level curve
- Why are these useful
- When do we see them in real life (way more commonly than expected)
- How to calculate and draw them myself
- **BRAIN BLAST** representing 4 Dimensional Objects using level curves.What a fantastic concept. What a fucking beautiful, breath-takingly abstract concept. When I discovered this in my textbook, my heart smiled. I just knew deep down, what to expect next. Its about the wonder and curiosity of the 4th dimension. That’s why I was left so amazed and awestruck. You can represent 4D objects in 3D contour lines, big whoop. Big whoop? First of all, no one says big whoop anymore. Just think about the Carl Sagan and the Flat Landers. Imagine we were pulled out of our 3D world and had a glimpse of what it feels like to be in 4D! Holy shit. Being granted X-Ray vision into all things 3D. How strange a concept. We would see in the side of human bodies, and the inside of the bones, and the insides of the insides of the bones.
And this is who I am. I’m someone who finds the awe in a subject like calculus, which is usually detested by student my age. Or its usually liked because you can get by with just memorizing formulas and how to do questions. But I wonder how many other people marvel in the human achievement of calculus. James Stewart said it best:
Calculus is an exciting subject, justly considered to be one of the greatest achievements of the human intellect. I hope you will discover that it is not only useful but also intrinsically beautiful.