The Whole and the Parts – The Series

I’ve written a number of posts where the main theme is a whole that is more than just the sum of the parts.  Whenever you have a whole, it is worth looking to see if the nature and the behavior of the whole is fully captured by looking at the sum of the natures and the behaviors of the parts.  Sometimes the whole is indeed exactly like the sum of its parts – the name we have for these kinds of situations is linear.   The behavior of linear systems is extraordinarily important, both practically and theoretically.  Though linear behavior sounds very simple, thinking about linear behavior and analyzing it will quickly get us into very interesting territory.  The posts on Groupings, Shopping List, and Vectors (accessible from here), is meant as an entry point into this territory.

In other cases, at least as important, there is something about the whole that is not quite captured by looking at the sum of the parts.   Though generally harder to analyze, there are fortunately lots of specific cases that are both of great practical interest and can be made sense of.

The Prisoner’s Dilemma – the classic example where what’s good for each is not what’s good for both – and they aren’t even competing for the same resources!

Feedback Loops – a feedback loop can make a bunch of parts into a whole, and give it new properties.

Packaging – The grocery store may let you buy one can out of a six pack, but won’t let you buy half a can.

Memory and Hysteresis – How do you make a whole that remembers something about its past?  It’s actually quite common.  We use a retractable ballpoint pen as a simple example.

Black Boxes – We enter into territory where we don’t know what the parts are that make up the whole.

You may also like my other blog, Avoid the Rush, where comparison of properties of the whole and those of the parts is a major theme throughout.

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About Bert Speelpenning

http://unlearningmath.com is my blog on math learning and math teaching. My background is in the high-tech computer software industry (I've got a PhD in Computer Science from the University of Illinois) and worked for Hewlett Packard, Silicon Graphics, Borland and finally for Microsoft till I left in 2000. I have since worked in the area of math learning, with students (7-9th grade) and teachers (elementary school level). I own an independent educational consulting business called Math Partners.
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