Sometimes all we need in life is a different perspective, a new angle from which we can view a problem. Once we see a phenomenon in a different light we may be able to see a different there, ergo a solution to a problem. An idea is analogous to a three dimensional shape in the aspect of sight and understanding. We cannot see all sides of the shape at once, we cannot ever fully understand the dynamics of a shape from one perspective. Only thinking about an idea from one perspective is limiting our true view of the idea. We exist from behind our eyes and truly only can have one view, and that is the view from the perspective of our ego. We as humans willingly let our ego blind us from the truth and duality of nature, because of the protection the ego offers us. We can rotate an idea analogous to rotating a shape, understanding the different facets of a phenomenon, developing an understanding that essentially generalizes through the domain different facets. This seems like a great idea to do, and in my mind it is, but we have to ask the question: If it is so beneficial, why don't more people do it? This type of thinking is mind expanding, but on the other side of the coin; ego stripping. We are programed to be reluctant to let go of comfortable ideas, we find it threating to see something from another perspective because of the evil that comes with it. Take politics, divisive especially in the year of 2020, all of us, democrats, republicans, or any other political affiliation, hold tight to our beliefs because the uncomfortableness you feel without them. That same force whispering in your ear to stay in your comfort zone limits you from a deeper understanding, generalization of the facets.
I think we all deal with this, subconsciously be that, my pursuit through writing this blog is to bring this idea though your subconscious and into the conscious, the realm of analyzation; problem solving. We can all benefit from realizing the problems we have hidden through years of ignoring, the way to understand is to generalize more broadly. Understanding to a broader extent may cause us initial discomfort but ultimately it is to our best interest to develop a deeper and more beautiful understanding. Now comes the implementation into artificial intelligence. Artificial understanding: the shine of our god given philosophy of thought though our imperfect minds and syntax onto our creations and in my case programs and algorithms. I have had the idea of the conceptualization of ideas as shapes in the mind of the machine previous to writing this blog. This idea is pretty far away from what everyone else is doing in the realm of deep learning research. Conceptualizing ideas as three dimensional shapes not explored in the domain of AI/DL/ML, but the rotation of three dimensional shapes is.
A mathematician by the name of Sir William Rowan Hamilton was in pursuit of a number system like the complex number system, but with an additional axis. His son would ask him every day, "Daddy, have you figured out how to multiply triplets yet?", and every day he would reply, "No, I haven't son". One day, as Sir Hamilton was walking across the Broome Bridge in Dublin, he had a shift in perspective. Sir Hamilton thought to himself that morning: what if I used a four dimensional number system instead of the three dimensional one? There lies, on the Broome Bridge in Dublin, Ireland; the fundamental formula for quaternions inscribed on October 12, 1843. The only sadness I have, is that Sir Rowan Hamilton will not be able to see his innovation of quaternions describe his own shift in perspective, the rotation of his idea described using the formulas he wrote down as a product of that conceptual rotation. I give you, a shift in perspective.