Moulton Lava

Moultonic Musings

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Saturday, March 02, 2013

Problem Solving and Problem Creation

When I woke up this morning, I was thinking about a standard method of problem-solving that I have used many times in the course of my professional career.

It's based on studying the exact opposite of problem-solving. It's based on the study of problem creation.

I'll give you two examples.

The first example comes from a branch of mathematics called Chaos Theory. Chaos, as you know, is the opposite of Order. Since the dawn of civilization, human societies have valued Order and disvalued Chaos. To achieve Order, humankind invented Laws. And so we have the cultural concept of Law and Order.

But in the middle of the 20th Century, an MIT researcher working on weather and climate models took up the mathematical problem of creating Chaos. He discovered the roots of Chaos, through which he could create all manner of Chaos on purpose, as easily as possible. He discovered the easiest way to create Chaos is to adopt a rule (known as a Recursion Law) and apply it over and over. Almost all systems of rules are capable of creating Chaos, simply by following the rules without deviation.

So what did Edward Lorenz discover? He accidentally discovered that Law and Order is not only a myth, the adoption of Laws is the single most reliable way to cause Disorder.

The second example comes from a study of collections of seemingly unrelated problems. So, for example, Buddhism is about solving the problem of Suffering. According to Buddhist insight, Attachment is the root of Suffering. Now take the problem of Violence. Most of the violence in our culture takes the form of Vengeance (or Revenge). And so we have Wars and Systems of Justice, both of which answer one kind of violence (Unlawful Violence) with another kind of violence (Lawful Violence). Violence, of course, causes Suffering. As one zooms out, one observes a large collection of inter-related problems, where the common practices adopted to solve one of the problems either backfires and makes it worse, or else causes a fresh instance of one or more of the other problems in the collection.

I'll skip here to the bottom line and give you a list of ten such inter-related problems, where our practices to solve any one of them tends to exacerbate or even cause one or more of the others.

The Ten Big Unsolved Problems in our culture are: Conflict, Violence, Oppression, Injustice, Corruption, Poverty, Ignorance, Alienation, Suffering, and Terrorism.

Now there are plenty of discussion groups focused on Problem Solving. But suppose we study just the opposite. Suppose we study Problem Creation, to discover the easiest and most reliable way to create one or more of the specific problems in the collection of dreadful problems, so as to generate a chain reaction in which we get more and more of each of the specific kinds of problems in the above list.

Here is my sure-fire recipe for generating all manner of intractable problems.

Start with equal measures of Fear and Ignorance. Mix well, and act impulsively or impetuously out of Fear and Ignorance. Voila! You have just created a magnificent chain reaction of all the world's most troubling problems. What could be easier?

But wait. You say you don't want all those problems -- problems of Conflict, Violence, Oppression, Injustice, Corruption, Poverty, Ignorance, Alienation, Suffering, and Terrorism?

Easy. Don't act out of Fear and Ignorance. Instead, openly disclose your Fears. Openly disclose your Ignorance. And then have some faith that others will come forward to allay your fears and cure your ignorance.

But who among us has the Courage to disclose our Fears? Who among us has the Intelligence to disclose our Ignorance?


Blogger Unknown said...

To your list of ten I add one more:


7:19 PM  
Blogger Moulton said...

Larry Lessig has called it obliviousness.

Others have called it apathy.

There are two obvious reasons people might be indifferent or apathetic.

The first obvious reason would be that they are simply unaware, which would be subsumed under the category of ignorance.

The second obvious reason would be that they have no influence or power, because they are kept out of the loop. That would be subsumed under the category of alienation.

Having said that, I do believe that lack of empathy is a serious issue in our culture, but the main reason for lack of empathy isn't indifference but the presence of antipathy, which would be subsumed under the category of conflict.

So the real challenge here is the ethical challenge of igniting passion to solve problems without igniting passion that ends up motivating unwise responses that only serve to exacerbate or spread an underlying problem, rather than extinguish it.

7:55 PM  
Blogger Higs; said...

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11:14 AM  
Blogger Moulton said...

Intentional inaction, amounting to bearing silent witness, is often the best option, especially when one is bewildered or perplexed by an unanticipated breach of expectations for which best practices are unknown.

The second best practice might be to simply tell the honest story of what went awry, as a personal memoir.

However, it may be necessary to disguise the story by converting it to piece of literary fiction, in the style of Dostoevsky or Dickens.

12:50 PM  
Blogger Higs; said...

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4:39 PM  
Blogger Jim said...

Can you cite the paper the MIT researcher worked on?

9:15 AM  
Blogger Moulton said...

There is more than one, but the first one dates back to 1963.

You can find a succinct list of the papers by Edward Lorenz in his Wikipedia biography, along with a discussion of how they relate to the development of Chaos Theory as we understand it today.

12:36 PM  
Blogger Higs; said...

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9:12 AM  
Blogger Higs; said...

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9:35 AM  
Blogger Moulton said...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other.

Here, your classical example would be to deform an inflated balloon, such as performers often do at children's parties.

Naively, one might think a simple sphere immersion would be to inflate one balloon around another, much like those nested Russian dolls.

But I gather the mathematical definition of immersion is not a simple idea like that, but something much more abstract and difficult to visualize.

So I'm entirely unclear on what a double sphere immersion is, or what is meant by a cusp.

In other words, the mathematics of homotopy mappings is way beyond my frontiers, and perhaps entirely inaccessible to me, notwithstanding my depth in other branches of mathematics.

Chaos Theory and Catastrophe Theory are much more accessible.

Here is James Gleick's quite understandable video explaining Chaos Theory.

9:54 AM  
Blogger Moulton said...

The Galen-Harvey Story is a bit like the Ptolemy-Copernicus Story.

There is a comparable story in human societal models. It begins with Hammurabi, but I don't know who to nominate as the Messianic figure who overthrows Hammurabi.

One can mention a sequence of contributors: Moses, Buddha, Lao Tsu, Hillel, Jesus, Gamaliel, Augustine, Maimonides, Beckett, Thoreau, Dostoevsky, Gandhi, King, Girard, Gilligan, Thich Nhat Hanh and many more.

Ultimately, I believe their work will be reified by rigorous mathematics, invoking Recursion Theory and Chaos Theory to elevate traditional Theology to Scientific Theory and Mathematical Theorem.

10:18 AM  
Blogger Higs; said...

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12:13 PM  
Blogger Moulton said...

Turning a sphere inside out seemed impossible, so I chased down the links.

Most of the videos are no longer to be found, but this page was telling:

Visualization of the Sphere Eversion

I was arrested by Step #1:

Push the South Pole through the North Pole

Huh? That requires that the sphere be punctured at the North Pole. A punctured sphere is equivalent to a test tube, a condom, or a sock.

It's trivial to turn a sock inside out.

In other words, the surface of the sphere is not a solid surface, but a mesh, as if it were a porous knitted sphere. Well sure, a sphere with a porous surface can be turned inside out.

It's no big deal to turn a balloon inside out if you do that before you blow it up and tie off the mouth. A balloon that has not yet been blown up is the same as a condom for the purposes of turning it inside out.

5:45 AM  
Blogger Higs; said...

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7:53 PM  
Blogger Moulton said...

Surfaces intersect geometrically. We're not talking about socks or balloon, but a double homotopic three-dimensional sphere.

I sort of get that, but it's also where I fell off the boat (or fell through the bottom of the hull).

I guess instead of a solid surface sphere made of atoms, where the electron clouds repel invading fingers that try to poke through the surface, this is more like a spherical wavefront, where one wavefront can effortlessly pass through another (the way two photons can pass through the same point in space without interfering with or ricocheting off each other).

In other words, the surfaces behave as if they are porous, so that one surface can weep through the pores of another surface.

With that revision in my mental model, a whole lot of magic becomes possible.

It's not that I'm disinterested in topology or homotopy, it's just that I've never studied it, and thus never thought about useful applications of the corresponding mathematical abstractions.

6:11 AM  
Blogger Higs; said...

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5:45 PM  
Blogger Moulton said...

"It’s easier for me to think of it with lines, where lines may intersect without perforating one another; so may planes and curved surfaces."

This is the subtle difference that makes the difference.

I guess I was somewhat misled by the glass Klein bottles which could actually hold liquids. The notion that the tubular neck of the glass Klein bottle could not merely pierce the sidewall of the Klein bottle but leave an open passage for the liquid contents to flow is the crucial discrepancy here.

In your review, I gather there would not be an open passage corresponding to a hole in the side of the bottle through which the tubular neck passes.

Your model is more like the 3-D models found in computer animation, where your avatar can effortlessly fly through surfaces that are supposed to represent solid walls.

In those 3-D models, sometimes they add the code that makes the walls solid and impenetrable, and sometimes they omit the code because they reason your avatar could never get near enough the surface to discover your avatar can walk through it as if it were a curtain of air.

12:03 PM  
Blogger Higs; said...

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1:08 PM  
Blogger Higs; said...

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3:08 PM  

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