complexity and order in evolution

[sol invictus]

We are taught to think of evolution as something special - a unique process which depends on the existence of life, mutations, genetic inheritance, and natural selection. It is this combination, the argument goes, which brings complex structures such as eyes, human brains, and Mozart symphonies into existence.

And yet when we look around, we see incredibly complex and intricate structures in the world that appeared without any of those ingredients. Snowflakes spontaneously form beautiful branching crystals with hexagonal symmetry, galaxies form from chaotic (and truly random) quantum fluctuations in the density of primordial hydrogen, and an incredible variety and profusion of stars live, age, and die according to a complex life-cycle. Is there any rigorous way to define how the products of evolution differ from these phenomena? Can we find a mathematical definition of the complexity we find so apparent (and so contentious)?

A place to start is information theory. One might take a DNA sequence and compute its Shannon entropy (which is a measure of how predictable the sequence is). The difficulty, though, is what to compare the result to. A truly random sequence of the same length? The crystalline structure of a naturally occurring ordered system, like a salt crystal or a snow flake? Compared to the first, DNA is ordered, but compared to the second it is random.

So how do we quantify the special kind of order brought about by evolution? Does it exist at all?

[69dodge]

Some more or less random thoughts:

What's important about evolved organisms is what they can do, namely, reproduce successfully in a given environment. This would be missed by just looking at purely informational aspects of their DNA. What's important is what is encoded, and not really how efficiently it is encoded. As an analogy, you'd miss pretty much the whole point of a computer program if you just calculated its Shannon entropy, considering it merely as a string of bits, without thinking about what computer it is intended to run on or what it does when run on it.

[kerikiwi]

Snowflakes and galaxies don't reproduce, either with or without mutation.

[rocketdodger]

And yet when we look around, we see incredibly complex and intricate structures in the world that appeared without any of those ingredients. Snowflakes spontaneously form beautiful branching crystals with hexagonal symmetry, galaxies form from chaotic (and truly random) quantum fluctuations in the density of primordial hydrogen, and an incredible variety and profusion of stars live, age, and die according to a complex life-cycle. Is there any rigorous way to define how the products of evolution differ from these phenomena? Can we find a mathematical definition of the complexity we find so apparent (and so contentious)?



The mechanisms of evolution specialize in changing complexity levels in the realm of "beyond the sum of one's parts." As such, virtually all of the products of evolution are more than the sum of their parts, and any measure of their complexity must take this into account.

The other phenomena you listed do not share this ability.

I don't know how to formulate that mathematically (it might require a new type of mathematics), but it seems to be what you are looking for.

[sol invictus]

OK, reproduction is a place to start.

Stars undergo supernovae, forming heavy elements that make more stars, some of a new and different type. Snowflakes melt, flow to the sea, evaporate, and reform.

While I'm sure we can come up with definitions of reproduction that exclude these processes, I'm not particularly interested in semantics. I'm after something more rigorous.

[sol invictus]

The mechanisms of evolution specialize in changing complexity levels in the realm of "beyond the sum of one's parts." As such, virtually all of the products of evolution are more than the sum of their parts, and any measure of their complexity must take this into account.

The other phenomena you listed do not share this ability.

I don't know how to formulate that mathematically (it might require a new type of mathematics), but it seems to be what you are looking for.

Exactly - I want to quantify that "beyond the sum of one's parts."

But wouldn't you say that starting from a region in a bunch of hydrogen gas in space that happens to be overdense by merely 1 part in 100,000, which much later collapsed, heated, formed a star, went nova, formed iron, formed a metal-rich star, formed Saturn with its rings... wouldn't you say that's more than the sum of its parts?

[Alric]

So how do we quantify the special kind of order brought about by evolution? Does it exist at all?

Its not a special kind of order. Its exactly the same kind of order. One thing that will help you is to understand snowflakes form in an instant and there is no selection process for their shape. DNA molecules in living organisms have been undergoing selection, replication and random mutations for nearly 4 billion years.

If snowflakes replicated and were selected for their shape you would have some awesome crystal structures in the end.

In general this complexity business is only of marginal use when applied to understanding evolution and its a bit of a straw man. It generally devolves into trying to answer the question; "how likely it is that a given sequence of DNA arises over time"? If we talk about a specific sequence the answer is "infinitesimal", another word for "miraculous". However, the correct question is what is the probability is of ANY sequence to arise. Then the answer is "probable" and a lot more mundane.

[sol invictus]

One thing that will help you is to understand snowflakes form in an instant and there is no selection process for their shape. DNA molecules in living organisms have been undergoing selection, replication and random mutations for nearly 4 billion years.

I was aware of that, thanks. :)

But that doesn't suffice - stars have been around for much longer than life (although not actually that much longer, proportionally). "Stars" in unstable configurations, which form randomly, are "selected" against - which is why all stars are round, for example, and probably why there are many binary star systems but not other configurations. There is a pretty well understood birth/death cycle as well, with some (evolutionary?) changes over time (like increasing metallicity).

The biggest difference I see is DNA, but as I said in the OP, I don't see how to quantify the information in it.

[Alric]

The biggest difference I see is DNA, but as I said in the OP, I don't see how to quantify the information in it.

Well. Good luck. But like I said before there is no difference and its quantification would be only marginally useful.

[rocketdodger]

Exactly - I want to quantify that "beyond the sum of one's parts."

But wouldn't you say that starting from a region in a bunch of hydrogen gas in space that happens to be overdense by merely 1 part in 100,000, which much later collapsed, heated, formed a star, went nova, formed iron, formed a metal-rich star, formed Saturn with its rings... wouldn't you say that's more than the sum of its parts?

Yes and no, depending on how you look at it.

Yes if you are looking at how the entity came about.

No if you are ignoring how it came about and only focusing on what it can do.

[sol invictus]

Yes if you are looking at how the entity came about.

No if you are ignoring how it came about and only focusing on what it can do.

You mean, in the sense that the human brain can do more things than the rights of Saturn?

Is that true, actually?

[rocketdodger]

You mean, in the sense that the human brain can do more things than the rights of Saturn?

Is that true, actually?

Using most of the definitions of "do" that a human would care about, I imagine.

Of course, it all comes down to what one actually means.

[Acleron]

Can we find a mathematical definition of the complexity we find so apparent (and so contentious)?

A place to start is information theory. One might take a DNA sequence and compute its Shannon entropy (which is a measure of how predictable the sequence is). The difficulty, though, is what to compare the result to. A truly random sequence of the same length? The crystalline structure of a naturally occurring ordered system, like a salt crystal or a snow flake? Compared to the first, DNA is ordered, but compared to the second it is random.

So how do we quantify the special kind of order brought about by evolution? Does it exist at all?

Perhaps looking at the DNA sequence is is the problem. Much of DNA only makes sense when transcripted into proteins using the triplet decoding system. This is similar to a computer program, the sequence of bytes appears pretty random until they are translated according to the op-code system for that processor.

Unfortunately, this approach doesn't go much further. The initial organisms, after proteins were produced, would be pretty organised. The mutation of genes would produce equally organised proteins (or death - natural selection). Temporary disorganisation can be produced by gene duplication followed by mutation of the second copy before those mutations produced anything useful.

Sorry, but the more I write, the more hopeless it seems.

[Alric]

And like I said before looking at the probability of a given sequence is the incorrect question. The question is the probability of any sequence that is the result of the general process to arise.

For example the probability that I will win the lottery is very low. But because of the lottery system, the probability that someone will win the lottery is comparably higher.

This is the main error of Dembski and others. For more information I recommend John Allen Paulo's "Irreligion".

[athon]

I'm not sure there is a 'special' order to biological evolution. Fundamentally there are rules which determine a process of selection. Sure, it's complex chemical selection, while with snowflakes it arises from simple rules of forces, and galaxies it arises from complex interactions of long-distance forces...but in the end, there is a process of combination and selection. We see similar 'design-like' patterns coming up with languages and economics as well, which come about through totally different means (but are also influenced by measures of non-intentional selection).

Athon

[sol invictus]

I'm not sure there is a 'special' order to biological evolution. Fundamentally there are rules which determine a process of selection. Sure, it's complex chemical selection, while with snowflakes it arises from simple rules of forces, and galaxies it arises from complex interactions of long-distance forces...but in the end, there is a process of combination and selection. We see similar 'design-like' patterns coming up with languages and economics as well, which come about through totally different means (but are also influenced by measures of non-intentional selection).


Perhaps you are right. But then isn't it ironic that so much effort goes into arguing about how possible or impossible evolution is? It's no different from any other process.

I still have the feeling that there should be some way to characterize the information in the genome which will distinguish it from more typical physical processes. But I really can't see what it is. One of the strangest things about information theory is the fact that a very efficient code (the kind of thing that might evolve into being after a long time) is indistinguishable from thermal noise. Kind of like what stars emit....

[Acleron]

Another thought.

Look for the preponderance of DNA sequences that code for the alpha-helix and beta-pleated sheets that provide the rough structure of proteins.

[Alric]

Perhaps you are right. But then isn't it ironic that so much effort goes into arguing about how possible or impossible evolution is? It's no different from any other process.

That's right. That's why the most vociferous people that insist this is an important question are those on the intelligent design camp. Actual scientists know how easy apparent complexity can arise in nature based on known and mundane physical laws.

[sol invictus]

Another thought.

Look for the preponderance of DNA sequences that code for the alpha-helix and beta-pleated sheets that provide the rough structure of proteins.

That would show up in a crude measure like entropy as a decrease from the maximum possible value (indicating some kind of order). To do better, one can use more sophisticated techniques - discrete Fourier transforms, for example, or various types of probability calculations and Monte Carlo simulations - to get a measure of how non-random the sequence is in some specific way, and I'm sure your signal would show up there.*

But finding some kind of order in DNA isn't enough to distinguish it as special, since it seems there's quite a bit more order in crystals, for example.


*Actually in the past I helped do some of those types of analyses, and the results are that DNA is very much not random - it has lots of not-so-obvious patterns which can be found statistically. There are some potentially very important applications, diagnosis of genetic conditions for example.

[jimbob]

Perhaps you are right. But then isn't it ironic that so much effort goes into arguing about how possible or impossible evolution is? It's no different from any other process.

I still have the feeling that there should be some way to characterize the information in the genome which will distinguish it from more typical physical processes. But I really can't see what it is. One of the strangest things about information theory is the fact that a very efficient code (the kind of thing that might evolve into being after a long time) is indistinguishable from thermal noise. Kind of like what stars emit....


Of course there is always a tradeoff between efficiency and redundancy. You might expect DNA to have some form of error-correction coding.

Slightly OT, but I'd say that imperfect self-replication in a finite system, is probably nescesary and sufficent for evolution. The fact that the system is finite means that eventually some of the variants will compete amongst themselves for resources, guaranteeing natural selection (not usually the only source), whilst the imperfect copying provides the variation.

[Meadmaker]

The biggest difference I see is DNA, but as I said in the OP, I don't see how to quantify the information in it.

I certainly can't give a numerical answer, but I can talk about the general manner in which information is quantified, and it applies to DNA, and us, as well.

A system has "more information", if more bits are needed to describe it. The key to deciding if lots of bits are needed to describe it is not the amount of information needed to exactly duplicate it, but the amount of information needed to create something which would be considered in the same class.

For example, to describe a "royal flush" in poker, I would say that there must be five cards. They must be a 10, Jack, Queen, King, and Ace, and they must all be the same suit. That takes longer to describe than "five cards" which is a random hand. My random hand may in fact be a royal flush, but that's not important, because when I change one of those cards into the seven of diamonds, I still have a hand of five cards. If I change a card in the royal flush to the seven of diamonds, I no longer have a royal flush. I need all the characteristics to describe the royal flush.

Likewise, if I have a few million carbon atoms, plus some hydrogen, oxygen, and nitrogen, I have a random mix of atoms. On the other hand, in order to describe human DNA, I have to have that many atoms, but in a specific sequence, an order. I can only change a small percentage of the base pairs at all and still come up with "human DNA". This contrasts with a pile of atoms, which is still a pile of atoms if I swish it around a bit, or change the mix of carbon just a bit.

Human DNA is also more complex than Jellyfish DNA because I have to use more bits to describe human DNA.

This notion of how many bits are needed to describe turns out to be mathematically equivalent to what fraction of possible states fit the description. i.e. Given millions of carbon, nitrogen, oxygen, and hydrogen (and some other stuff for good measure, I'm guessing), the are gazillions of ways to arrange them into a pile of atoms, but only billions of ways to make them into Human DNA.

This sort of "order" is quite different from the order of a crystal, because the order of a crystal comes simply from repeating a single pattern over and over. I can say NaCl, repeated many times, and I have described a salt crystal.

I could go on and on, but you might already understand everything I've said, in which case I've missed the point, or I might just take a long time to say it.

I will say, to anyone reading and interested in the subject, that I "got" the whole concept of information theory and its relationship to complexity and to the laws of thermodynamics after reading "The Recursive Universe", by Poundstone. I had managed to pass the tests during undergraduate physics, and barely understood the implications during the engineering classes that touched on the subject, but until that book, I didn't really understand it.

[nescafe]

A place to start is information theory. One might take a DNA sequence and compute its Shannon entropy (which is a measure of how predictable the sequence is). The difficulty, though, is what to compare the result to. A truly random sequence of the same length? The crystalline structure of a naturally occurring ordered system, like a salt crystal or a snow flake? Compared to the first, DNA is ordered, but compared to the second it is random.

Sounds like you want Chaitin (http://umcs.maine.edu/~chaitin)'s information theory, not Shannon's.

[sol invictus]

Of course there is always a tradeoff between efficiency and redundancy. You might expect DNA to have some form of error-correction coding.

That's an excellent point, and DNA does indeed have such mechanisms. A perfectly efficient code has no redundancy and therefore no tolerance for errors. DNA by contrast is quite redundant. So that's the problem, in a nutshell - biological information is neither very efficient nor very redundant. So what makes it so special - if anything?


I could go on and on, but you might already understand everything I've said, in which case I've missed the point, or I might just take a long time to say it.


Well, it sounds like you're talking about the standard definitions of information. My problem is that a salt crystal has a much lower entropy than a DNA sequence, but a random sequence has a much higher one. So how can we use that to identify DNA sequences as anything out of the ordinary?

Sounds like you want Chaitin (http://umcs.maine.edu/~chaitin)'s information theory, not Shannon's.

I've never heard of him. I'll have a look - thanks!

[Dancing David]

Perhaps you are right. But then isn't it ironic that so much effort goes into arguing about how possible or impossible evolution is? It's no different from any other process.

I still have the feeling that there should be some way to characterize the information in the genome which will distinguish it from more typical physical processes. But I really can't see what it is. One of the strangest things about information theory is the fact that a very efficient code (the kind of thing that might evolve into being after a long time) is indistinguishable from thermal noise. Kind of like what stars emit....


Well, that is the nubbin right there.

Some people want to give humans a privileged position, be they creationists or people who believe in transcendent consciousness.

Evolution and biology are physical processes that are the same as other physical processes. Consciousness is no different than a rock rolling down a hill.

;) (Franko/Wraith alert?)

[sol invictus]

Evolution and biology are physical processes that are the same as other physical processes. Consciousness is no different than a rock rolling down a hill.


So you don't think there's anything at all special about biological evolution as opposed to any other physical process?

[Roboramma]

It's an interesting question.

On the one hand, it's true that evolutionary processes occur by the actions of the same forces that cause everything else. There is nothing inherently special about biology in that regard.

But I think that there is something distinctive, and meaningfully so - adaptiveness. Birds wings undergo the developmental processes that they do, and form the finished product that they do because those same processes and outcomes formed wings that were good at flying in their ancestors. The wing is an adaptation. Saturn's rings are not.

[sol invictus]

But I think that there is something distinctive, and meaningfully so - adaptiveness. Birds wings undergo the developmental processes that they do, and form the finished product that they do because those same processes and outcomes formed wings that were good at flying in their ancestors. The wing is an adaptation. Saturn's rings are not.

Couldn't I argue that all stable structures that exist in the universe are the result of a kind of selection? Saturn's rings are very special - they have very particular properties and lots of internal order (kind of like feathers on a wing). If they didn't have those properties they wouldn't be stable, and would either fall apart entirely or tend towards a stable configuration. When conditions change (which happens only very slowly for a planet, but it does happen) the rings will "adapt" and change too.

So is there really a difference?

[Roboramma]

Couldn't I argue that all stable structures that exist in the universe are the result of a kind of selection? Saturn's rings are very special - they have very particular properties and lots of internal order (kind of like feathers on a wing). If they didn't have those properties they wouldn't be stable, and would either fall apart entirely or tend towards a stable configuration. When conditions change (which happens only very slowly for a planet, but it does happen) the rings will "adapt" and change too.
I don't see how. Saturn's rings don't have heredity. Selection only works with heredity.
What you're suggesting is that saturns rings exist because they are stable. That's not particularly interesting - if they were something else, they would be something else.

Regarding what I said about adaptiveness - what I think is interesting about it is how it can answer certain questions.
For instance, if I were to ask, "why is this particular crater on the moon shaped in this particular way?" the answer would have to do with the size of the object that created it, the speed at which it struck the moon, and the properties of the material that the moon is made up of.

On the other hand, if I asked about the shape of a bird's wing (or a human hand, or the antenae of an ant) the answer would have to do with what it could be used for. Now, obviously not everything about living things is adaptive. But living things do have adaptations, and those are the things that meaningfully make life different from other processes.

There's nothing magical about that of course - nuclear fussion is different from chemical reactions in that it is defined by two light weight elements 'fusing' to create a new, heavier one. There is a distinction there, but it's certainly not a magical one.

[sol invictus]

I don't see how. Saturn's rings don't have heredity. Selection only works with heredity.

What do you mean? You can't mean discrete generations - clearly some kind of continuously changing system in time can evolve. For example, rather than an individual or individual species, take all the biomass on the earth at any given time as the system in question. Wouldn't you agree that that evolves? But if so, it's awfully similar to any other physical system that changes smoothly in time. "Heredity" is then just standard physics (the state of the system at any time is determined by the state the moment before).

What you're suggesting is that saturns rings exist because they are stable. That's not particularly interesting - if they were something else, they would be something else.

It's the same with wings, no? A population of birds with bad wings would be unstable and wouldn't survive, just as some stuff in the rings that gets into the wrong orbit will be ejected.

Regarding what I said about adaptiveness - what I think is interesting about it is how it can answer certain questions.
<snip for brevity>
On the other hand, if I asked about the shape of a bird's wing (or a human hand, or the antenae of an ant) the answer would have to do with what it could be used for.

"Used for"... I'm not sure I follow, unless you're referring to intelligence of consciousness. Otherwise what's the difference between saying "The bird uses its wings to fly" and "Saturn uses its rotation to keep its rings stable"?

So maybe focusing on intelligence is a good idea. The only problem is, there are plenty of things (like plants or algae) with pretty minimal intelligence that evolve.

[Alric]

Take this from the biologists. For evolution four things are required and sufficient:

1. Replication
2. A bit of change
3. Selection
4. Repeat over a long period of time.

The rings of Saturn were formed only by selection. The right particle was at the right time in the correct orbit, or selected.

Intelligence would be the worst thing for focus because most living organisms do not have intelligence. Evolution is all about survival of genes, nothing else.

[sol invictus]

Take this from the biologists. For evolution four things are required and sufficient:

1. Replication
2. A bit of change
3. Selection
4. Repeat over a long period of time.


1. Particles in the rings split (and perhaps join, I don't know). Some are ejected; new ones are captured. I don't know if rings themselves can appear or disappear, but I wouldn't be surprised.

2. There is plenty of change over long time scales - orbits are perturbed for various reasons, for example. And of course over very long time scales planets and their rings are created and destroyed due to environmental changes.

3. We've agreed that's there.

4. The universe isn't old enough for some things to have repeated many times, but for example there have been at least several generations of stars, and the newer ones are quite different from the first generation.

So it seems that if there are differences they're a matter of degree rather than anything fundamental. And even roughly quantifying the degree of difference appears to be very difficult.

This is kind of the ultimate anti-creationist point of view to take, I think: not only is evolution possible, it (and its products) are no different from any other physical process we see around us.

[Belz...]

The mechanisms of evolution specialize in changing complexity levels in the realm of "beyond the sum of one's parts." As such, virtually all of the products of evolution are more than the sum of their parts, and any measure of their complexity must take this into account.

The other phenomena you listed do not share this ability.

I don't know how to formulate that mathematically (it might require a new type of mathematics), but it seems to be what you are looking for.

Just a question: how can anything be more than the sum of its parts ?

[hammegk]

Some people want to give humans a privileged position, be they creationists or people who believe in transcendent consciousness.
Perhaps "life" occupies the privileged position?

Evolution and biology are physical processes that are the same as other physical processes.
That's one viewpoint. What is your answer to my question above?


Consciousness is no different than a rock rolling down a hill.

;) (Franko/Wraith alert?)
Ya "think"? ;)

I do agree evolution/biology/a-rolling-rock are the same is the correct answer under your apparent view.