Is complexity measurable?

[Chillheimer]

Hi!
I was wondering if there is a measure for complexity.
I mean the complexity of something in our real world. like (let's go big right away) the complexity of life.
like in here:


Anyone know of scientific attempts to measure the complexity of life?

[kram1032]

The problem with this is that there is no clear definition of what "complexity" - even "complexity of life" even means. You gotta ask this question for each very specific type of complexity. And there are various existing measures.
One simple measure of "the complexity of the universe" simply is the comparison between the very longest and the very shortest length scale you actually can observe. - This is meant to be a global definition so it'd require you to see the entire universe (not just the bits that were reached by light), so it's not actually measurable from our perspective, but the idea behind it would be that, if there is a large spectrum of potential scales, more of those scales will inevitably be inhabited and, thus, the whole thing will overally look more complex.
If you tried to apply this concept to a fractal, you'd find a complexity value of infinity.

However, this definition is meant to specifically be applied to physical space. In a mathematical system you can trick it out incredibly easily. Just consider three points, two of which happen to have the same coordinates. The associated complexity will be infinity, no matter where the third point lies, as long as it doesn't also share the same coordinates.

Another idea might be information-theoretic: How much information is required to describe a given system exactly? The correct measure of this turns out to be the von Neumann Entropy. And furthermore, that entropy, which is a purely mathematical construct, if you plug in the various thermodynamic potentials, just happens to coincide with the various common definitions of physical entropy.

In both those cases, iirc, one problem is that they fundamentally assume closed systems, but for life to even happen you almost by definition require an open system (Our planet constantly gets extra energy from the outside - namely, predominantly, solar radiation)

It's a.... complex issue riddled with either weak, brittle definitions, or strong, not necessarily realistic assumptions.

Nonetheless, you'll be able to find a lot of stuff about various ideas of complexity by simply googling.

[lycium]

I think complexity of life roughly correlates with the amount of "awake" matter, such as brains or computer chips, and these require a lot of energy (besides the associated costs of transporting our meat machines around). So we can measure a civilization by how much energy it uses, which leads us to the Kardashev Scale.

PS. Everyone should read Accelerando by Charles Stross, along with the technical companion

[kram1032]

Also an interesting metric, however I can see efficiency being a potential problem. It's probably rather unlikely but it's technically possible for us to reduce our energy needs and in turn shut down some energy producers (like power plants) simply by switching over to more advanced power savings tech. In such a(n admittedly very artificial) scenario, I'd argue we become more advanced as well as more complex while our power potential actually sinks.
For most actually occurring scenarios it should be a fine metric though.
Still, I'd love to see a mathematically solid definition without such edge-case problems. And to date I don't think that actually exists yet.

[Tglad]

Not sure if complexity is measurable but I feel the need to object to the diagram... It is natural that your knowledge of the near past and your opinion of the importance of events in the near past is greater than that in the distant past. The graph simply reflects this temporal proximity bias.

[Chillheimer]

Hi everyone & thx for your answers.
I had googled a bit and had already found this: https://en.wikipedia.org/wiki/Category:Measures_of_complexity
So yeah, there obviously is no easy answer to this question.

I don't think the Kardashev Scale is the right one (at least for me). What about computers becoming more and more efficient, using less energy while providing exponentially more computing power?
Or if you stay with life, why should an elefant (who definitely burns more energy, be more complex than a human being.

Though I find the Kardashec Scale fascinating, the set 3 steps seem somewhat arbitrary to me..
I'll have a look at Accellerando, sounds very interesting, thx for the tip.

@Tglad: I think you mix two things that don't belong together. The timespans between major events definitely is shortening, and (depending on what you choose as "major events") that this shortening seems exponential.
I think the diagram says it all, this has nothing to do with perception and knowledge of the past. The main steps of evolution are speeding up in an exponential way and I believe Moore's Law is just the technological, exponential continuation of this biologic evolution.

regarding the singularity - I think we are actually right in it. With humans connecting over the internet, we have become like one giant brain. mankind as a single new lifeform. and we are its braincells.
no single braincell is capable to see/compute/understand what is going on overall. we've lost it, it's on the next level, and we remain on the previous level of evolution. that's the reason why we still can live normal lives. but the world rushes by faster and faster. and as amoebas still exist and don't care about higher species like reptiles, we still exist and are just a tiny part of the new big thing.

edit: here's kurzweils answer to a similar critique. he's much better in describing this than I could ever be: http://www.kurzweilai.net/response-to-the-singularity-is-always-near

but I don't think this is bad. My life is still very happy, and it's great to be connected to all this.

[Chillheimer]

maybe I should add the reason why I ask this question.
I am taking that online course from complexity explorer and just learned how to calculate the dimension of a shape.

<a href="https://www.youtube.com/v/MhsEZ5i3brs&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/MhsEZ5i3brs&rel=1&fs=1&hd=1</a>

magnification factor^D = number of small copies

it's no problem to do this calculation for a line, a plane or a cube. but what about the next dimension, which for me is time.
and how could we calculate then the fractal dimension of e.g. the observable universe, what would be the magnification factor, what the small copies?

or when you see every generation of a species as a single iteration of fractal evolution (as I see it) what's the magnifictaion factor..
yeah, I know, pretty far out again..

[cKleinhuis]

wait for the lesson when they introduce to you the fractal dimension or was it already included afterwards ?!

the whole concept is quite striking, if you have a good understanding of the integer dimension principle you have a good starter for fractal dimension, and yes, its a measure for complexity

you will learn the following: the border of the mandelbrot set has dimension of 2 <- wtf ?  


now that you learned that the dimension of a line is 1 and that of a square 2 ... what about the inbetween dimensions you will learn, dimension=1 is just true for a straigt line, as soon as the line is not straight its dimensions grows above 1

[kram1032]

YouTube embedded player rant:
Why can't these embedded players be feature complete? It's so annoying. While fullview now works (most of the time) what still doesn't is the ability to set playback speed. I still have to actually change to YouTube to enable that.
/rant