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

Saturday, February 18, 2017

On the cost of elegance

"In character, in manner, in style, in all the things, the supreme excellence is simplicity.” — Henry Wadsworth Longfellow
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Prof T:
“Hey! Did you find an apartment you like?”

Prof. C:
”Well, I've found several, but they are all well out of my price range.”

Prof. T:
”What exactly are you looking for?”

Prof. C:
”Elegance.”

Prof. T:
”Ah, well, elegance will cost you; it always does :-).”

Prof. C:
”Tell me about it :-). I know it is because the material they use is very expensive. It looks great and lasts very long. But this explanation in itself is not particularly elegant.”

Prof. T:
”I believe elegance comprises simplicity and order. An elegant system, be it a mathematical model, a computer program, or an apartment, requires its creator/developer/designer to put a lot of effort into the work; effort in terms of battle against entropy. This battle has to be won; or there would be no elegance. When we see such a system, we often fail to realize the extent of the effort put into winning the battle against entropy. It is only natural for every system to eventually surrender to entropy.

Prof. C: ”I guess that fate is inevitable.”

Prof. T: ”Right. All we can do is to prolong the duration of the battle. I think the systems we perceive as elegant are those for which substantially more effort is put into the design and development phase, as compared to the effort required during their operation. For example, a well designed and properly built apartment requires significantly less maintenance effort than one with poor design and/or construction. The same goes for computer programs.”

Prof. C:
”Nice. Interesting interpretation of the second law of thermodynamics. Although, it would be nice if you'd come up with an original idea one of these days ;-).”

Prof. T:
”LOL. I know. But there's still hope. The meaning of the term 'original' might not be as obvious though; most innovations are just combinations of existing ideas, aren't they? ;-)”

Prof. C:
”And welcome to the wonderful world of combinatorics :-).”
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"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius — and a lot of courage to move in the opposite direction.” — Ernst F. Schumacher