Thread: Complexity

Then is this a square?

__ .. __
| |__| |
|........|
|_____|

Since three of the sides are redundant to complete the shape?

And drewmandan, is a static television less complex than a working airhorn?

No, because this shape has a different area and perimeter of a square, and has more sides. It is not the same as a square.

A redundancy would be having two sides that run overtop of each other-- They are the same. Which is what you are basically doing with 14 = 7+7, etc.

Originally Posted by Omnius Deus

And drewmandan, is a static television less complex than a working airhorn?

I was referring to the static itself, not the television. I just needed a common everyday example of true randomness. Way to miss the point, by the way.

No, because 7+7 is two numbers, without one, you can't complete the equation because 7=\=14

Okay drew I bite what the fuck is your point?

Originally Posted by Omnius Deus

No, because 7+7 is two numbers, without one, you can't complete the equation because 7=\=14

Okay drew I bite what the fuck is your point?

You've missed the point.

7 + 7 = 14, not 7.

Since 7+7 and 14 are equivalent, they are equally as complex.

Writing 14 out to be 7+7 is an example of redundancy. The systems are equal.

I agree. Writing 4 is equally as complex as 2+2 because they are equal.

But I guess it depends on your definition of complexity.

You could say that:
2[1.566-0.566]/2+1=2[1.566-0.566]/2+4/2-2

is more complex than 2=2

or you can say it is exactly as complex because they are equal.

complexity
Noun
pl -ties
1. the state or quality of being intricate or complex
2. something complicated //OH WOW

Originally Posted by Omnius Deus

Okay drew I bite what the fuck is your point?

In my first post I gave a reasonable definition of complexity as something inversely proportional to entropy. What has more entropy, a tv showing static, or a tv showing the evening news? Obviously the tv with static. Hence, by my rough definition, the tv showing the evening news, as a system, is more complex than the one showing static.

And I'll also touch on the triangle example. Consider the space of all equilateral triangles. What varies in that space? Size. The length of the sides is the only thing that can vary among equilateral triangles (obviously barring stupid stuff like colour, which applies to isosceles as well). Now consider the space of all isosceles triangles. What can vary? The two side lengths can vary independently, and the angles vary too but as a function of side length.

Now, going back to entropy, imagine the two sets of triangles were like molecules, vibrating along their degrees of freedom. You will see an equil. triangle getting bigger, smaller, bigger, smaller, etc., and an isosceles getting bigger and smaller, but also getting more and less stretched, because it has 2 degrees of freedom, which is more than 1. Now, the definition of entropy is that more degrees of freedom means more entropy. Hence, more degrees of freedom means less complexity by my definition. And that's why I say equil. triangles are more complex than isos.

Originally Posted by xXSomeGuyXx

I agree. Writing 4 is equally as complex as 2+2 because they are equal.

But I guess it depends on your definition of complexity.

You could say that:
2[1.566-0.566]/2+1=2[1.566-0.566]/2+4/2-2

is more complex than 2=2

or you can say it is exactly as complex because they are equal.

complexity
Noun
pl -ties
1. the state or quality of being intricate or complex
2. something complicated //OH WOW

I would say that except by a select few individual's definitions, 2[1.566-0.566]/2+1=2[1.566-0.566]/2+4/2-2 is more complex than 2=2.

I would also say that two blocks side by side supporting one block 2 feet in the air is more complex than one block supporting one block 2 feet in the air (another example of redundancy).

Originally Posted by drewmandan

In my first post I gave a reasonable definition of complexity as something inversely proportional to entropy. What has more entropy, a tv showing static, or a tv showing the evening news? Obviously the tv with static. Hence, by my rough definition, the tv showing the evening news, as a system, is more complex than the one showing static.

And I'll also touch on the triangle example. Consider the space of all equilateral triangles. What varies in that space? Size. The length of the sides is the only thing that can vary among equilateral triangles (obviously barring stupid stuff like colour, which applies to isosceles as well). Now consider the space of all isosceles triangles. What can vary? The two side lengths can vary independently, and the angles vary too but as a function of side length.

Now, going back to entropy, imagine the two sets of triangles were like molecules, vibrating along their degrees of freedom. You will see an equil. triangle getting bigger, smaller, bigger, smaller, etc., and an isosceles getting bigger and smaller, but also getting more and less stretched, because it has 2 degrees of freedom, which is more than 1. Now, the definition of entropy is that more degrees of freedom means more entropy. Hence, more degrees of freedom means less complexity by my definition. And that's why I say equil. triangles are more complex than isos.

What about a system which has many degrees of freedom that vary widely, but all in a structured way?

And so would I.

Originally Posted by Xaqaria

I would say that except by a select few individual's definitions, 2[1.566-0.566]/2+1=2[1.566-0.566]/2+4/2-2 is more complex than 2=2.

I would also say that two blocks side by side supporting one block 2 feet in the air is more complex than one block supporting one block 2 feet in the air (another example of redundancy).

Well, the system would be equally complex as a larger block, but separately they are less complex.

That's what I THOUGHT you point was. And my example still has value.

If something has entropy, and therefore freedom to change, then isn't it potentially more complex than a completed system?

Originally Posted by Omnius Deus

That's what I THOUGHT you point was. And my example still has value.

If something has entropy, and therefore freedom to change, then isn't it potentially more complex than a completed system?

Potential is meaningless. One stem cell has the potential to create entire organs, but that doesn't make it more complex than a single skin cell.

Originally Posted by Omnius Deus

That's what I THOUGHT you point was. And my example still has value.

If something has entropy, and therefore freedom to change, then isn't it potentially more complex than a completed system?

That's not what entropy is. Entropy is disorder, or in other words, a measure of how inaccurate a model of the system will be. You're using the word "change" as in some sort of stochastic process, which is completely out of context.

But why is entropy less complex? We just accept that as a given, if something is complete it is more complex than something that is incomplete?

Originally Posted by Omnius Deus

But why is entropy less complex? We just accept that as a given, if something is complete it is more complex than something that is incomplete?

I never used the word "complete". Entropy is randomness. If you want to start calling randomness complexity, then go ahead, but good luck deriving any objective meaning out of it.

I'm only asking a question. You're drawing arbitrary lines to put things on a scale from simple to complex and they have no logical backing. I'm only asking why, why is the line there?

I'm using words like function, complete, etc... because I'm assuming we're not just talking about math here, but systems in reality, too. In reality just because something has no perceivable pattern doesn't mean it has no pattern. Just because something doesn't function properly doesn't mean there's not a system in place that's more complex than a functioning one.

What is more complex:

f(x) = (2x - x)/(x²)

or

f(x) = (3x - 2x)/(1 - x)

Originally Posted by A Roxxor

What is more complex:

f(x) = (2x - x)/(x²)

or

f(x) = (3x - 2x)/(1 - x)

The second one, I think. I count 5 operations in the second one and 4 in the first.

Originally Posted by A Roxxor

You've missed the point.

7 + 7 = 14, not 7.

Since 7+7 and 14 are equivalent, they are equally as complex.

Writing 14 out to be 7+7 is an example of redundancy. The systems are equal.

14 and 7+7 are not equal, they only have an equivalent mathematical value. I think you can easily tell that the two differ in many ways.

Originally Posted by Xaqaria

I think you can easily tell that the two differ in many ways.

Like, in terms of pixels, or...?

You always have to define the complexity space before you can make comparisons. For example, consider "17" and "17". If we're judging complexity in terms of mathematical meaning, then they're equal. If we're talking about the number of bits required to fully describe their colour, then "17" is more complex than 17. So you have to be rigorous when talking about this stuff, otherwise you get nowhere.

Originally Posted by drewmandan

Like, in terms of pixels, or...?

You always have to define the complexity space before you can make comparisons. For example, consider "17" and "17". If we're judging complexity in terms of mathematical meaning, then they're equal. If we're talking about the number of bits required to fully describe their colour, then "17" is more complex than 17. So you have to be rigorous when talking about this stuff, otherwise you get nowhere.

If you'll go back and read the OP, you will find that is the purpose of the thread. If you want to quantify complexity by attributing a mathematical value to every system, thats fine; but then how do you compare say, the complexity of a Dali painting to a Monet? I'm looking for a scale of complexity that could apply to all systems and structures. Mathematical value may have a place in the comparison but it is far from a complete picture.

Originally Posted by Xaqaria

14 and 7+7 are not equal, they only have an equivalent mathematical value. I think you can easily tell that the two differ in many ways.

No...

7+7 is an alternate way of writing 14-- That is a redundant system. It doesn't count.

This doesn't JUST apply to mathematics, but it is an easy way of conveying the basic idea.

Originally Posted by Xaqaria

If you'll go back and read the OP, you will find that is the purpose of the thread. If you want to quantify complexity by attributing a mathematical value to every system, thats fine; but then how do you compare say, the complexity of a Dali painting to a Monet? I'm looking for a scale of complexity that could apply to all systems and structures. Mathematical value may have a place in the comparison but it is far from a complete picture.

You'll notice, however, that both the possible definitions of complexity I gave have similar notions, they only differ in the thing being measured.

Originally Posted by drewmandan

You'll notice, however, that both the possible definitions of complexity I gave have similar notions, they only differ in the thing being measured.

So perhaps you could phrase it in such a way as to encompass both options, thus bringing us closer to an all encompassing set of criteria.

Originally Posted by A Roxxor

No...

7+7 is an alternate way of writing 14-- That is a redundant system. It doesn't count.

This doesn't JUST apply to mathematics, but it is an easy way of conveying the basic idea.

Okay, maybe you don't think it counts, but that is an opinion and not a fact. I personally can find many differences between the structure {7+7} and the structure {14} . A pretty simple difference is, they take a different number of bits to represent in binary code. As far as I'm concerned, the only thing that is truly equivalent with a system is itself, and only at the given moment of comparison.


Using xei's information concept, perhaps complexity can be expressed in one way as a ratio of largest quantity of novel information a system can generate over smallest quantity of information needed to fully represent it.