Complexity

Below are two images I created using algorithms.   Which image is more complex, A or B?   Or are they equally complex?

AB

Now here are two more images.   Which is more complex, C or D?   Or are they equally complex?

CD

For the first question I assume that most people will choose B.   For the second question I assume that most people will choose D.   There is a certain sense within which the second question could be answered in that manner, but not when paired with the first question, and I will explain why in a moment.

More and more I am noticing an ambiguity in the use of the idea of complexity.   I have observed it in both average joes and in the most venerated of scholars.   They will use the word "complex" to refer to very different ideas, sometimes within the very same sentence.   This is not a good, for this vague inconsistency is allowing irrational propositions to sound sensible.

I created the quiz at the beginning of this essay to demonstrate that inconsistency.   In the first question, B is clearly more complex than A.   But the second question is not as straightforward.   In one sense the images look very different.   And yet they were built with identical algorithms.   The only difference is that with image D the range of the equation was greater.   You could increase the scope of the algorithm to encompass millions of pixels and the pattern would never really change.   In essence, compared to the first image, the second image is just more of the same.

If you were to reduce images A and B to their most simple definitions, (the equations used to generate them), B would still be more complex than A.   But if you were to reduce C and D to their simplest definitions, their complexity would be identical. (  Note that while what I am talking about is similar to the idea of Irreducible Complexity, it is not the same thing.) 

I am not going to try to define complexity in this essay.   That is a vast and complex subject.   I am simply bringing attention to a particular slice of complexity.   I will however, note that usually definitions of "complexity" involve the idea of multiple parts connected to each other.   What I am showing in this essay is that there is an important distinction between a system comprised of many identical parts and a system that is comprised of many parts with different essential attributes.   To better explain this I will return to my example of the images.

AB

Most people would say that image B is more complex than image A, and yet the images themselves contain the exact same number of pixels.   To relate that idea to my last paragraph, they have the same number of parts.   And yet when the human mind perceives image A it can summarize it as simply "a square comprised of pixels all of the same color", while the human mind cannot summarize image B into such a neat package.

Another way to illustrate this would be to take a car and glue hundreds of small random objects onto its surface.   In one sense that car would become more complex because it would be comprised of many more parts than it had been, but since none of those parts would actually be essential to the car's functionality of getting its occupants from point A to point B, in that sense the system of that car would not be any more complex than it had been.

This ties back to my last post on how Process = Product.   When I created the algorithms that generated those images, I could have had one of those algorithms additionally check my email and defrag my hard drive, which would have made the algorithm much more complex but as far as the image that it generated, the image would not have changed.   Within the context of the generated image those additional functions would be superfluous.   Mathematically, that would have been the equivalent of taking the following equation:

x = 5

and changing it into:

y = 1
x = 5 + y - 1

In one sense the second equation involves more parts, but in another sense it is just as simple as the first equation.

So in summary, all I am doing in this essay is trying to define and describe these two different dimensions of complexity.   Ideally I should have a term to describe the first type and a term to describe the second type but I don't yet have any good terms for these ideas.   I'm hoping that perhaps a reader of this essay will know of terms for these ideas that already exist and inform me of those terms.

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On Production

Most of the work I have ever done has involved industry.  I like to make stuff.  And not only do I like to make stuff, I am also fascinated by the processes and tools used to make stuff.  I am always trying to refine my creation methods and develop new tools to support me in my creative endeavors.  

Sometimes I have heard people say things like "I don't care how you do it, just get it done and "all we're concerned about is the end product."  I think there is an important point in those statements, but I think their language is misleading.  It is true that the work involved in creating a product is simply a means to an end; the only reason you're doing what you're doing is for the end result.  However, the statements above imply more than just that, and what they imply is an inaccurate relationship between process and products.  

Through my studying of production and its many forms, I have come across a principal that at first looks absurdly simple and yet is more deep and meaningful the more I think about it.  This principle can be described as the following:

Process = Product

In other words, the process is the product.  They are interchangeable.  For instance, if any change is made to a process, due to the laws of causality, that change in the process will be reflected in the product.  Likewise, if I make any modifications to the product, I have, in essence, equally modified the process.  

Now, someone might say "Wait a minute! What if I have an assembly line and I replace one of the workers on the assembly line: Bob, with a new worker: Sue.  I would have just then modified the process without modifying the product."  But that argument is misleading.  If Sue performs her job so similarly to the way Bob did that there is no change to the product, then the process was not really modified.  But if Sue does not perform her role in quite the same way that Bob did so that the product changes to some degree then yes, the process was modified.  The scope of the process that is associated with that product only extends as far as any factors that actually affect the final product.  For example, within the described context of this scenario, the name of the person on the assembly line has no impact on the product.  

This principle can be seen reflected in the moviemaking process.  If a producer is making a movie, he doesn't simply look for the all-around "best" people to make a movie; he hires people that will most likely achieve the specific vision he has for that movie.  If it is a dark movie, he may look for a composer that tends to write dark music.  If it is an action movie, he may look for a director who has a passion for action movies.  

It is the same idea with molds.  I once was on a tour of a business that produces molds that in turn are used to produce various mechanical parts.  Near the beginning of the tour, the owner of the business explained to us tourists that a mold is not simply a hollow cutout.  I don't remember his exact words, but I think his general point was that a mold was all of the things that went into defining the final part that was produced.  

I think in his explanation he was mainly referring to the different physical parts that surrounded the traditional idea of a mold, though if one were to continue along in the same direction he was heading, that entire business is, in a sense, one giant mold.  For example, while the secretary may not be a direct influence on the molds produced by that business in that her operation does not define the distinctions between one mold that is produced from another, her function still influences the state of the molds that are produced by that business.  Unlike the specific physical parts of a mold that define the product's shape, her function is necessary for the operation of that business and thus defines a more general property of all of the molds: whether or not they exist.  

I have found this principle of "Process = Product" very useful in approaching artistic endeavors.  For example, I've heard that Stephen King generally writes his stories from beginning to end without having any idea what he will write next.  This results in stories that have a very natural, uncontrived flow, but at the same time lack a strong sense of purpose and cohesion.  As for me, I do not write stories in a linear fashion.  I start with the overall mental state I want my audience to arrive at through reading the story and then work backwards finding events and elements that, when put in the right combination, will achieve the desired effect upon my audience.  This tends to result in the opposite of a Stephen King novel: stories that have a strong sense of purpose and cohesion and yet feel contrived and surreal.  

Each of those methods of story construction result in very different types of products.  Sometimes I think people see writing as simply a matter of sitting down and putting a lot of time and effort into putting words on paper, and yet it is much more complicated than that.  The selection of the process that an author uses in how to go about putting words on paper puts strong constraints on what the final product can be.  

It is possible to change method halfway through production, but if you do so keep in mind that what you have done is selected a process that is a compound of both your first and second methods.  Even if you start from scratch when you switch to the second method, the product would probably still be influenced by your work using the first method, and thus the time spent using that first method would still technically fall within the scope of the process that resulted in the final product.  In other words, the use of both methods shaped the definition of the finished story.  

I could go on and on giving examples, but I think that should give a basic idea of the relationship between a process and its product

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The Magician of Chance

"There have always been ghosts in the machine. Random segments of code, that have grouped together to form unexpected protocols. Unanticipated, these free radicals engender questions of free will, creativity, and even the nature of what we might call the soul. . . . When does a perceptual schematic become consciousness? When does a difference engine become the search for truth?" - from "I Robot" (2004).

While that is a cool quote, I chose that as a preface because it summarizes what this essay is confronting. I am amazed at how the general populace of this age have somehow acquired the idea that if a system becomes complicated enough and implements enough randomness it eventually takes on mystic properties. Perhaps the leading scientists of this age know better, but if so, they are doing very little to correct the ideas of the general public.

This concept is throughout our media. How many superheroes have gained their powers through some catastrophic accident, usually involving toxic sludge? I haven't yet come across anyone who actually believes that such a thing could happen. I propose that people generally assume that scientific accidents don't give people superpowers because they've never heard of it really happening. But I've never heard anyone questioning why that wouldn't happen.

Then there's robots. Isaac Asimov pioneered the idea that human advances with AI would eventually surpass our understanding; that due to the incredibly complex programming within the robot's circuitry it would become smarter than it was designed to be. Asimov's robots were generally benevolent, but this idea has been most prevalently seen throughout media in the scenario of robots advancing to the point of taking over humanity, such as in movies like The Terminator and The Matrix.

So where is the line beyond which systems get so complicated and random that fantastic stuff starts happening? Is there such a line?

There are two main ingredients to this belief system: chance and complexity. Hopefully in a later essay I will address complexity, but in the remainder of this essay I will be briefly addressing chance and its relative: randomness.

chance –noun
1. the absence of any cause of events that can be predicted, understood, or controlled: often personified or treated as a positive agency: Chance governs all.
2. luck or fortune: a game of chance.
3. a possibility or probability of anything happening: a fifty-percent chance of success.

ran·dom –adjective
1. proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers.
2. Statistics. of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

Here I will demonstrate a very simple analysis of chance. Many of you have probably already heard this. Let's take, for example, a dice roll. A person throws the die onto the table and it lands on a random side. But is it really random? If you knew how that person's brain was interacting with the nerves and muscles and that person's hands and arms and knew all of the physical factors with the air resistance and how the die bounced along the table surface; if you had all the factors involved in that die toss you could use mathematics to precisely calculate what side that die would land on.

The only thing that makes that die roll seem like chance is the fact that we don't have all the factors. Chance is purely a subjective term dependent upon the subject's knowledge. Since we do not have all the factors, we gather together all the factors we do have, organize them into equations, and determine what the most likely outcome would be.

The process of estimating odds like that is called statistical probability. With a dice roll the odds are generally evenly divided between the six sides, but most of life is much more complicated, such as calculating the probability that this essay is actually worth the time spent to read it. That would be far less straightforward. Assessing probability is a foundational part of human decision-making. It is what allows us to make useful decisions without being omniscient.

I should clarify that randomness is not the same thing as chance. The essence of chance revolves around the issue of predictability, while randomness can exist independent of that issue. For example, it is possible, with the right knowledge and tools, to accurately predict what numbers will be generated by a computer in a game of solitaire. That is because those numbers are generated through a very mechanical and man-made process involving time and lookup tables. And yet even if you were to accurately predict the resulting numbers, they would still technically fall within the definition of randomness, for whether or not you could predict them, they would still have no definite aim, reason, or pattern.

In all these examples what I'm trying to do is unmask the mystery surrounding chance. Neither chance nor probability nor randomness are sources of power that can be harnessed. They are not natural forces. They do not cause things to happen. They are simply ways of looking at life that we have developed to help us do the best we can with the limited knowledge at our disposal.

(Now, as an aside, I am open to arguments that those actually are forces in that ignorance, the thing from which they derive meaningful existence, could possibly be considered a force and arguably even a good force at times, for when it comes to things like exploration, discovery, and many forms of entertainment, the value of such things is dependent on ignorance.

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Science is not Reality

sci·ence /ˈsaɪəns/ [sahy-uhns]
–noun
1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
2. systematic knowledge of the physical or material world gained through observation and experimentation.
3. any of the branches of natural or physical science.
4. systematized knowledge in general.
5. knowledge, as of facts or principles; knowledge gained by systematic study.
6. a particular branch of knowledge.
7. skill, esp. reflecting a precise application of facts or principles; proficiency.

There is a myth I've been coming across in one blog after another that equates science with reality. It is possible to have overlap between the two, but they are never the exact same thing. Reality is the way things are. Science is the way we think things are.

Right off, if anyone is going to use proper English, to say that your beliefs are based on science is absurd. That is because many people throughout the world have reached many conflicting scientific conclusions. To claim that your beliefs are based on science is to say that the foundation for your beliefs is contradictory.

But I don't think most people are using the proper English definition of the word "science" anymore. When people refer to "science" they are referring to some implied subdivisions of science; not the collective views of all scientists but the views of specific scientists. Most commonly, I've found that when people refer to science, they are referring to popular opinion. Popular opinion should not be underestimated and should be carefully weighed, but just because a large number of people believe a fact does not change reality. There was a time when practically everyone believed the world was flat, and yet that did not make it so.

Science is always changing because people keep aquiring new data that shows that previous theories were innacurate. Reality never changes, but science is always changing. With that in mind, should a person be so confident in claiming science as the foundation for their beliefs?

I've been browsing the web for various people's responses to the movie Expelled. Whether or not Intelligent Design or Evolution are viable beliefs, I'm amazed at the number of people who are against the movie and yet prove it's central point. People have become so entrenched in their own worldviews that they equate that with reality. Evolutionists are not the only people who have ever ceased to question their own perspectives, Creationists througout history have done that as well, but that fact does not mitigate the responsibility of the present scientific establishment.

(As a quick clarification of my title, even though science and reality are not the same thing, science is still a part of reality. Even if someone were to believe a lie, in one sense that lie would still be a very real, genuine lie. So whether or not a scientific conclusion lines up with reality, science is still very real if understood within its context of being a classification of human knowledge.)

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Survive or be Useful?

Last week I saw the movie Expelled, and I just saw it again this evening. That movie has made a big impact on me. In a later post I might go into more detail on that, but for now I want to focus on relating software design to the theory of biological evolution.

I do not know much about biology. But I do know a lot about system design, and the rules of system design are as universal as the rules of logic. Humans are systems. Dogs are systems. Cells are systems. Molecules are systems. Everything in life can be broken down into systems and systems within systems.


Here are some examples of system philosophy:

A system cannot produce a system more advanced than itself.

Mankind has never yet been able to design a system that improves itself, and there is no evidence to suggest that such a feat is possible.

Hierarchy is the best organization of systems, and all of life can be neatly conceptualized into hierarchies.

Modularity is an essential property of a good system.

Those are just some examples of the abstract world I love to study.

From a systematic point of view, evolution is illogical in multiple ways. Many scientists claim that all the evidence points to evolution, but that is simply not true. They are only referring to specific evidence. I am talking about general evidence which, if they wish to maintain rationality, they must be accountable to.

Like I said, there are multiple ways in which evolution is systematically illogical, but to apply modularity I will only address one of them in this post. And the first is this: evolution, or at the least the most popular interpretations of evolution, are intrinsically based upon natural selection. I would argue that, from a systematic point of view, natural selection could never account for the current state of the universe.

To begin, I need a definition of natural selection. Unfortunately, I've had a hard time finding a definition of natural selection. It seems that much of the people in this world do not understand what a definition is anymore and are busy defining the class that natural selection is inside instead of the attributes of natural selection that distinguish it from everything else. Both of the terms "evolution" and "natural selection" are so ambiguous that it makes it very challenging to argue against evolution.

Whatever the case, the common trend I've seen in most explanations of natural selection is "survival of the fittest"; the idea that the organism with the best ability to survive in it's present environment will continue to exist after the weaker organisms go extinct.

And therein lies the rub. The driving factor within natural selection is survivability. To an evolutionist, the most important value an organism can have is how well it can maintain its existence and propagate. That sounds nice in theory, but in the real world good systems do not work like that. In the study of systems, it quickly becomes evident that the best systems are when the existence of organisms is maintained based upon functionality, not how well that organism can survive over its fellow organisms. Natural selection leads to anarchy. Good system design leads to community.

Functionality does play a role in the theory of evolution through symbiotic relationships, but that is still only a fraction of what is needed to produce a good system. Within natural selection collective functionality is subservient to individual survivability. How often will an employer hire people based upon how well that person will outlast his fellow employees? I've never seen it. An employer hires people based upon their usefulness to the company. Now, a useful employee will last longer in that company than a useless employee will, but notice that in that scenario the survivability is derived from the functionality, which is the reverse of natural selection. Throughout the bulk of existence functionality reigns. However, there are places in human experience where survivability is prioritized over communal usefulness. Some examples are: Slums, prisons, mafias, orphanages, beaucracies, etc.

A system is a collection of organisms working together to accomplish a common goal. If at least some part of that goal is not beyond the scope of that system, then that system is useless. In programming terms, it is a node with inputs but no outputs. It takes but doesn't give. Natural selection does not care if a system is useful or not. In a world of natural selection, it would be perfectly plausable to have useless systems thrive while useful systems vanish.

There is a funny sense in which evolutionists are like lukewarm Christians. It is a common trap for Christians to fall into thinking that being a Christian only matters on Sundays, and the rest of the week they live a life largely disconnected from the religious beliefs they claim to hold. Many Christians have a sense that God was sort of a thing of the past; that he was more real in ancient times than at present.

Evolutionists in general are the same way with their beliefs. They believe the laws of evolution applied to the "millions and millions of years" that led up to the present, but don't really consider those laws to be in effect within their moment to moment lives. "The world was developed by organisms fighting against each other, but now all those organisms are working together." Evolutionists put so much effort into justifying how evolution can explain the way things came to be that they don't put any effort into justifying how evolution can explain how things maintain their operation now.

If the laws of natural selection suddenly came into effect to the degree that evolutionists claim that they are, the human body would tear itself apart in competition. My heart and my lungs have a symbiotic relationship, but do they know that? My heart does not need my hand in order to function, so why doesn't it just stop pumping blood to my hand? But of course that is absurd. The organs of the body work in harmony. They are not competing with each other and no one except perhaps some biologists question that. But if natural selection is true, then they should be competing with each other. If you believe in natural selection than you should be afraid that your stomach would quit passing nutrients to your intestines because food passes through the stomach first, making the stomach the more powerful of the two organisms. If you say that is absurd, I agree with you, natural selection to that degree is absurd. If you say that natural selection does not work that way, then I will point out that if natural selection is not a universal law then there is no way it can account for every step of biological development.

As another example, take green evolutionists. I have heard many say that man has upset the balance of the ecosystem. But if they believe in evolution then there is no such thing as a balance of the ecosystem. To say such a thing is to suggest that all of these animals killing and devouring each other actually results not in a system of natural selection but in a system of natural harmony. That if humans had not come along there would actually be some state of status quo.

To further explore that, let's say there were only two species on the planet, the eaters and the eatens. Since the eaters live off of the eatens, the eaters are the more powerful of the two species, and yet they need the eatens to survive. Now, what would happen if the eaters wiped out the entire species of eatens? They too would go extinct. Thus it would be in the best interest of the eaters to keep the eatens alive.

And yet that is not natural selection. To keep the eatens alive would be to value their functionality over their survivability. They are more useful than they can survive. But if what evolutionists say is true and nature is in fact blind then in such a case both species would be wiped out. For the eaters not to wipe out the eatens would require an assessment of the larger picture. In short, it would require intelligence.

I think I'll stop for now. This isn't even touching the tip of the iceberg, but it's enough to start. As a quick closing point, natural selection is an inherently selfish theory. It proposes that the development of life as we know it was driven by exclusive selfishness (not simply thinking about yourself, but only thinking about yourself.) I believe in the Bible, and it teaches that our selfishness is not exclusive, but is derived from our functionality. As John Piper would say, "God is most glorified in us when we are most satisfied in him" and "God is the only route to final and lasting happiness". While evolution does not line up with systematic evidence, God does.

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