After some great feedback email and conversation, I'm going to elaborate a little further from my previous post. First and foremost, my colleague, Max pointed out the tangent is equation is dy/dx not dx/dy (I am often suffering from dyslexic tendencies in both writing and speech). Next, Max reminds me setting it to zero is for finding the horizontal tangent. Please don't tell my Physics professors I messed up!
Next, everybody I know named, Andy, brings up questions on thinking beyond 2D and 3D. What of 1D, 4D, and beyond?
Let me start by qualifying that my response may be more conjecture than scientific fact. I trust those much smarter than me will correct my thinking with the solid facts :-)
Now, let me try to classify the dimensions:
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1D
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Acting without thinking. When someone cuts you off in traffic and you release an explicative, they can't usually hear you and your explicative doesn't correct their behavior, but it sure makes you feel good. |
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2D
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Using logical inferences to draw a valid conclusion (a line from before). If the sun comes out today, then it will be warm. Note, not all valid arguments are sound. |
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3D
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Using valid logic and in pursuit of true premises to draw a sound conclusion that may not be absolute, but possibly a framework that encompasses many (ideally, all) valid perspectives (a plane from before). |
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4D and beyond
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Beyond logical inference to creatively discover truths that would otherwise be obscured by logic alone. Einstein with his many theories is an example here. |
Being a 2.5D thinker at best, I do not believe multidimensional thinking is linear in any way nor do I propose a pragmatic path to get oneself there. I simply am basing my conjecture on observation of those whom I observe to practice the art. Consider the non-linear curve as shown:
Stacked side by side:
This might imply two things:
- Multidimensional thinking has a “sweet-spot”
- There exists a threshold – which I refer to as the “threshold of human comprehension”
The latter imposes a whole new debate. There are those who would imply anything and everything can be explained, however, due to what ever limitations exist in our complex minds, we cannot comprehend everything.
l might suggest that individually, our personal threshold, moves up and down as we learn, mature, grow, etc. However, I would also suggest that while our personal thresholds are relatively dynamic, there exists an absolute limit to what we as biological beings can comprehend. I firmly believe we are yet to even come close to seeing that threshold, but there are times when we see a glimpse of it and have to take things "on faith".
Posted
06-09-2009 6:10 PM
by
Jim Wilt