Friday, February 24, 2017

On dimensions and perspectives

Prof. T: “Have you seen my book on the history of science?
Prof. C: [pointing to a bookshelf] “Over there
Prof. T: “Oh, nice. You added a new shelf. Are all these history books?
Prof. C: “That’s right. I moved all my history books here. Isn’t that what history is? A collection of books? ;-)
Prof. T: “I suppose that is one way of looking at it :-). I tend to see history as a collection of facts and experiences from which we can learn. I guess what one makes of history depends on one’s perspective.
Prof. C: “I’m glad you mentioned the term perspective. Just the other day I was thinking about how each observer can bring their own perspective, and how that affects the conclusions one draws.
Prof. T: “Indeed. I think it speaks to the complexity of the phenomena we observe. A phenomenon can be viewed from multiple perspectives, just like a geometric object can have multiple dimensions; each with a different face or facade.
Prof. C: “Hmmm. So then it can be argued that most phenomena in real life are not amenable to simple explanations; true insight can only be gleaned by taking multiple perspectives into consideration.
Prof. T: “Right. Just imagine us scientists making conclusions by analyzing just a single dimension in a high dimensional space, and ignoring all the other dimensions. Except for in certain specific situations, that would lead to disastrous results.
Prof. C: “I wonder though, in history, politics, social interactions, etc., how come most of us find it extremely difficult to view certain situations from more than one perspective? Any perspective other than one’s own seems alien, and often wrong.
Prof. T: “That is a very important question; one we should all ask ourselves all the time.
Prof. C: “Imagine a world where a person could completely understand another’s perspective. One could step into anyone else’s shoes and see the world through their eyes. Perhaps such an individual would see that we, as humans, have more in common with each other than we realize. Perhaps such an individual would be able to appreciate the fact that differences that move us farther apart from each other are, for the most part, merely differences in perspectives; and that the true picture comprises all the disparate perspectives.
Life, it seems, is a complex, high dimensional problem. Unless we learn to appreciate this complexity and to navigate the high dimensional space, there’s little hope we’ll learn how to make things better. Peace is a solution that lies in this high dimensional space. Perhaps complex systems science provides the method to find the solution.
Prof. T: “Ah, a super hero with the power to put herself into other’s shoes; shall we talk to the folks who write comic books ;-)?
Prof. C: “:-)

Prof. T:
“There’s certainly no doubt in the significance of studying phenomena as complex systems. Nevertheless, it occurs to me that perhaps the answer to your question lies in the analogy to the term dimension, as used in mathematics. We know how difficult, and at times intractable, it is to solve a high dimensional problem. So we make use of dimensionality reduction. Solution to the problem in reduced dimensions then becomes feasible.
Perhaps it is the case that in real life, we just find it simpler to look at phenomena from a single perspective. Perhaps we often fail to realize that doing away with other perspectives results in loss of information; information which might well be pertinent. We seem adept at following the path of least resistance.
Prof. C: “To peace, dimensions, complexity, and perspectives.
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"Our soul is cast into a body, where it finds number, time, dimension. Thereupon it reasons, and calls this nature necessity, and can believe nothing else.” — Blaise Pascal