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I don't understand why this is so profound. I knew Euler's formula was a trig formula simply by looking at it. I don't know why there needs to be this complex e

I don't understand why this is so profound. I knew Euler's formula was a trig formula simply by looking at it. I don't know why there needs to be this complex explanation of where it came from where its obvious that it comes from trig and the concept of a unit circle. The problem is that reliance on intuition doesn't prove anything and its very deceptive. You end up having to store several cases of explanations instead of deriving one through a proof. For example, one would intuitively think dropping a heavy object and a light object would conclude with the heavy object hitting the ground first which is not the case. This is just one example. I'd much rather derive things the traditional way and not be duped by "intuitive" explanations. Because ones intuition is often different from natures.

jonsen 8y ago
Intuition is not an absolute thing. Intuition changes as we learn. Sometimes we learn things without building an accompanying intuition. This post is about building a sound intuition for something learned.
- jshowa3 8y ago
  That's nice. I didn't say there was no value in intuition. I just said it was unreliable and I demonstrated an example of why its unreliable. Its better to focus on solutions that don't rely on intuition because intuition is based solely on experience and often can't be applied to everything. This is why there's a strive to find general solutions to things. Intuition can help you, but you should not base your understanding off it. Intuition can lead you astray easily as in my example. People just assumed it was correct for many years until Galileo actually proved it through experimentation. In fact, I found this explanation way more complicated than just stating that you are performing trigonometry in two different domains. Your sine is scaled by an imaginary value and your cosine is scaled by a real value. The radius equates to an exponential. When you move it pi units you get sin = 0, cosine = -1 which you use algebra to get Euler's identity. You don't need to introduce complex intuition in order to get it. Intuition is often a crutch people use to try and think they understand something and just blame others when they don't get it much like this post. If intuition was so important, why not submit it as a legitimate mathematical way of proving things?

jonsen 8y ago

Intuition is not an absolute thing. Intuition changes as we learn. Sometimes we learn things without building an accompanying intuition. This post is about building a sound intuition for something learned.

jshowa3 8y ago
That's nice. I didn't say there was no value in intuition. I just said it was unreliable and I demonstrated an example of why its unreliable. Its better to focus on solutions that don't rely on intuition because intuition is based solely on experience and often can't be applied to everything. This is why there's a strive to find general solutions to things. Intuition can help you, but you should not base your understanding off it. Intuition can lead you astray easily as in my example. People just assumed it was correct for many years until Galileo actually proved it through experimentation. In fact, I found this explanation way more complicated than just stating that you are performing trigonometry in two different domains. Your sine is scaled by an imaginary value and your cosine is scaled by a real value. The radius equates to an exponential. When you move it pi units you get sin = 0, cosine = -1 which you use algebra to get Euler's identity. You don't need to introduce complex intuition in order to get it. Intuition is often a crutch people use to try and think they understand something and just blame others when they don't get it much like this post. If intuition was so important, why not submit it as a legitimate mathematical way of proving things?