Emergent Properties, Abstraction, and Reductionism
by machtI wrote a post a couple years ago on the topics in the title and I thought I'd repost it here in light of all the discussion on the topic.
In my last post, I talked about how the nature of science is to make abstractions. That is, when scientists try to make general theories about something they strip the phenomenon of all its "unnecessary" qualities and properties and only look at the relevant ones. For example, if I want to come up with a general theory of projectile motion, I don't have much need for information about what my projectile is made of or how much it costs or what color it is. Very often, I won't even care what shape my projectile is (I'll just assume it to be a point-mass). All I'll be concerned about is the initial velocity of the projectile, it's mass, the force of gravity at my experiment location, its initial angle of motion, and the height it falls. In all likelihood, I'll make a further abstraction of the motion into vertical and horizontal components of motion and look at those separately. And I haven't even begun to mention things like the legal properties of the projectile (maybe it's a hollow-point bullet and not legal in some places) or the biological properties of the projectile (maybe it's a human cannonball).
Abstraction is a vital and necessary part of doing science. But it can be a problem if we forget that abstractions are being made and we end up mistaking the abstraction for the reality.
But this is precisely what I see a lot of people doing, especially in the area of "complex systems." (For purposes here, I'm going to use the term complex systems to refer to those areas of research that include complexity theory, chaos theory, dynamical systems, self-organization, and others.) Complex systems have found a home in everything from biology to meteorology to economics to cognitive science.
According to Steve Talbott, complex systems aim for both generality and abstraction:
"The quest for generality dictates this resort to abstraction. To arrive at generalizations regarding phenomena, we have to strip away all the differences between the phenomena, looking only for what they have in common. This stripping away makes it possible to assign different things to the same class (for example, street signs and redwoods), and once we have done this we can, without ambiguity, count and measure the members of the classes we have formed and reason mathematically about them (for example, formulating laws about their height)."
One of the main goals of complexity theory is to be able to treat everything from earthquakes to deer populations to brain neurons in a similar way with similar mathematical algorithms. So this aim for more and more generality leads to greater abstraction, such that we don't have to know about the actual phenomenon and objects we are studying. All we have to know about are the mathematical abstractions.
One of the major themes of complexity theory, is that very complex behaviors develop from relatively simple foundations. Very simple mathematical formulas can often lead to unpredictable and erratic behavior over a long period of time. There seem to be two groups of thought surrounding these ideas.
The first group is reductionistic. They say that in theory these complex behaviors can be explained by these simple foundations. They say that in theory the universe is just a bunch of atoms and ultimately everything (human brains, deer populations, hurricanes, etc.) is explainable in terms of atoms interacting with other atoms. The only reason we don't do this, they say, is because it is impractical. I have deep problems with this view. There is no explanation for how, for example, a person appreciating a piece of art could be explained in terms of quantum mechanics. They'll admit that we can't explain economics in terms of atoms interacting with each other and we probably never will, but it is impossible "in theory." Sometimes they call themselves "hierarchical reductionists" because they say that even though in theory things could be explained in terms of physical properties, it is much easier and time-effective and efficient to use "higher-level" explanations for more complex interactions. This whole view seems to me like the neighbor kid who says he has a rare baseball card in mint condition in his house but he can't show it to you because he doesn't want to ruin it's mint condition. In other words, the person who holds this view says that reductionism works but he can't show you that it works, you just have to take his word for it.
The second group is anti-reductionistic. They think that the complex interactions between these simple parts are actually more than the sum of the parts. Somehow emergent properties arise from the parts. These properties aren't found in any of the parts. This idea is sometimes used to explain human consciousness. The human brain is made of neurons. No single neuron is conscious, but when millions and billions of neurons are interconnected in complex networks, consciousness emerges. This consciousness is more than the neurons and their interconnections - there is truly a new phenomenon here. I find this view to be lacking, also. As Talbott points out, "It is hardly clear, from the current literature, what this emergent whole is thought to be, beyond the sum of its parts." What, exactly, is this "more" in the phrase "more than the sum of the parts?" Where does it come from? None of these types of questions ever seem to be answered.
I think there is a better way than both these approaches. Talbott, again, highlights what is generally wrong with using complexity theory in these ways,
"There are doubtless interesting ways to elucidate the power laws we can abstract from diverse phenomena. It's just that the act of abstraction here has been so severe — so many aspects of the phenomena we were looking at have been left out — that our discoveries, while interesting in their own right, will tell us almost nothing about these particular phenomena. The scholar who is seeking to understand the population growth of Cairo is much better advised to explore the relevant cultural, social, political, economic, geographic, and ecological realities bearing on this one place than to dwell on the elegance of a straight-line graph showing the frequency of occurrence of cities with different population levels. It's not clear who among students of particular phenomena will find much use, or much revelation, in that graph.
Explanations that do not depend on specific details will fail to elucidate those details. If, at the outset of our investigations, we strip away every concrete particular we can, then we will hardly arrive at any profound understanding of concrete, particular phenomena. But what else is there to understand? It was the whole concern of the key figures of the Scientific Revolution to shun the abstract cerebrations of the medieval schoolmen and open their eyes to the world around them. Should science reject this stance now, preferring (in Bak's words) "to free ourselves from seeing things the way they are"
The problem with a scientific method based on maximum generalization and abstraction is that the more it succeeds - that is, the more general and abstract its results become - the shallower they tend to be. They tell us less and less about the particular contexts we wish to understand. …
In our drive toward generality and abstraction, we end up with what we ask for. If, for example, we are determined to reckon only with what is generally true of both living organisms and systems of inanimate, mineral objects, we will end up seeing only the inanimate, mineral aspects of living organisms. We will get a theory that "connects" diverse things, but in the process loses the things we are connecting."
Talbott then goes on to talk about the problems with "emergent properties,"
"When your scientific work repeatedly brings you up against vaguely conceived "emergent" phenomena — phenomena that seem to arise from out of nowhere — you might reasonably wonder whether your models and explanatory mechanisms have omitted something important. While most complexity theorists seem undisturbed by this thought, I have been suggesting above that the omission has in fact been as radical as it could possibly be: what the models tend to leave out is the phenomenal world as such, with all its contingencies and with all its causal, or generative, powers. To these investigators, therefore, all actual phenomena are likely to appear emergent simply because all phenomena present a qualitative fullness that has intentionally been stripped from the theoretical apparatus employed to explain them."
Talbott's solution is to rethink how we do science. Physical reductionism completely removes qualities from science. Some people try to "slip them back in" by appealing to "emergent properties." Other's just say that "in theory" these qualities are fully explainable in terms of the physical, but refuse to tell us how. Talbott says that science must be qualitative in nature and that we must "face qualities up front, wrestling through to an understanding of their proper place in the scientific enterprise."
January 28th, 2007 at 8:21 pm
A good point to keep in mind.
An example is helpful. Snowflakes and DNA both exhibit complexity. The use of the word complexity conveys a misleading sense of shared properties in this case. One can predict snowflake formation by specifying conditions that are a prerequisite to it. The exact shape of any particular snowflake may be beyond the predictive capacity of theory but there is a plug-in aspect to the explanation. Plug-in the temperature and related weather conditions and the forces of nature associated with snowflakes form a coherent core for theoretical explanations.
Contrast the complexity of snowflakes with DNA. While DNA can certainly be described chemically, if we wish to describe its biologically functional nature we look not to forces of nature, but rather to a concept known as natural selection. The complexity of functional DNA is linked to the selective value of its constituent codons. Therein lies a problem for any complexity theory seeking to explain DNA's origins. For selection to be part of a viable theory, DNA must already have an encoding nature, a means of securing information from the destruction of environmental factors and a means of replication. Or if the foregoing is lacking one must at least be able to specify a physical process by which replication of a nucleic acid would occur and a criteria by which "copying errors" would be selected.
The nature of the differences between two distinct phenomenon become obscured by a word- complexity.
Comment by Bradford — January 28, 2007 @ 8:21 pm
January 28th, 2007 at 9:36 pm
Hi macht,
There appears to be a typo in your post:
Don't you mean "possible"
Comment by keiths — January 28, 2007 @ 9:36 pm
January 28th, 2007 at 11:58 pm
One line of reasoning that I think worth exploring is anti-reductionism in modern mathematics. With Godel's incompleteness we have truths not reducible to underlying axioms. Given that physics is presumed to have a mathematical foundation, it flows then that we ought to expect non-reductionistic physical phenomena.
Mathematics is both a mix of reductionistic truths and non-reductionistic truths. Both have validity, but neither encompases the most complete description. I would expect the same of physics given that physics is presumed to be inherently mathematical.
Comment by Salvador T. Cordova — January 28, 2007 @ 11:58 pm
January 29th, 2007 at 12:41 pm
Did Talbott have a suggestion on how to integrate the qualitative with the quantitative?
Comment by TomG — January 29, 2007 @ 12:41 pm
January 29th, 2007 at 3:25 pm
Sounds like to me these hyper-abstractionists are trying to come up with an emergentist theory of everything. How one would do that without some sort of coupling with qualitative phenomena is beyond me. I suppose it is understandable that they would love not to struggle with the myriad of specific qualitative issues, but like Talbott I would have to wonder if anything they came up with was relevant to real life. Reminds me of string theory.
I think that science is in a real quandary now with the recognition that emergent properties that cannot be deduced from fundamental properties. If that cannot be done, doesn't science start looking more like engineering. For instance, the rigidity in metals is not predicted or explained by the properties of single atoms or molecules. It is an emergent property. Now in engineering the modulus of elasticity can be measured for a metal and then the dynamics of rigidity characterized. But that is more of a description than explanation. For many scientists the inability, in principal, to discover something fundamental that explains later complexity would be devastating.
And according to some scientists things are even worse. Emergentists can be divided into a least two groups. The epistemological emergentists just claim that everything ensues from the bottom up, but that its too complex for humans to deal with all the variables. On the other hand, there are ontological emergentists like Nobel physicist Robert Laughlin who claim that in fact even fundamental properties may be emergent. Here's a quote from "A Different Universe":
Paul Davies is saying something very similar with regard to mathematics.
Here's another very intriguing statement from Laughlin talking about Einstein's relativity being emergent:
Now I don't think that Laughlin is talking here about a designer of life, but many ID proponents would agree that there is "something beyond" that is at least partly responsible for how life plays out.
Comment by Steve Petermann — January 29, 2007 @ 3:25 pm
January 30th, 2007 at 9:50 pm
Also in 1999:
Sunny Y. Auyung (A total babe!) wrote
http://www.creatingtechnology....
See the Pubs
http://www.creatingtechnology....
And
Carlson J.M., Doyle J., Highly optimized tolerance: A mechanism for power laws in designed systems.
PHYSICAL REVIEW E 60 (2): 1412-1427 Part A, AUG 1999.
We introduce a mechanism for generating power law distributions, referred to as highly optimized tolerance (HOT), which is motivated by biological organisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. We suggest that power laws in these systems are due to tradeoffs between yield, cost of resources, and tolerance to risks. These tradeoffs lead to highly optimized designs that allow for occasional large events. We investigate the mechanism in the context of percolation and sand pile models in order to emphasize the sharp contrasts between HOT and self-organized criticality (SOC), which has been widely suggested as the origin for power laws in complex systems. Like SOC, HOT produces power laws. However, compared to SOC, HOT states exist for densities which are higher than the critical density, and the power laws are not restricted to special values of the density. The characteristic features of HOT systems include: (1) high efficiency, performance, and robustness to designed-for uncertainties; (2) hypersensitivity to design flaws and unanticipated perturbations; (3) nongeneric, specialized, structured configurations; and (4) power laws. The first three of these are in contrast to the traditional hallmarks of criticality, and are obtained by simply adding the element of design to percolation and sand pile models, which completely changes their characteristics.
http://www.cs.sfu.ca/research/...
Fascinating subject to me and I wonder, macht, that it doesn't attract more attention. (Or maybe everyone's thinking about it?)
I have long attempted to get IDers interested in HOT… To no avail.
One problem that I see for ID (or the Dembski-brand of ID) is that like "complexity theory," it reduces complexity to a (statistical) law and robs complexity of all its wonder! Complexity is either generated randomly or an "act of God," and their all the same to me.
"Complexity theory" has a real problem–it hasn't been investigating complex systems at all!
Properly, complexity theory and its application, science, is the domain of biologists and… designers.
They have the science "down pat" (contrary to what Talbott seems to imply). What they don't have is a theory.
Comment by Rock — January 30, 2007 @ 9:50 pm
January 30th, 2007 at 11:48 pm
macht wrote:
macht,
As a fellow engineer, I'm a bit surprised to hear you make this argument. I don't know what kind of engineering you do, but in my field of integrated circuit design this kind of hierarchical reductionism is indispensable, well-grounded, and not at all controversial. Every IC designer is a hierarchical reductionist.
An integrated circuit can be viewed at many hierarchical levels:
As
1. A collection of atoms.
2. Interconnected regions of doped silicon.
3. Transistors.
4. Switches (idealized, simplified transistors).
4. Gates.
5. Multiple levels of modules, where a module is composed of a combination of lower-level modules.
Noone would dream of running functional simulations at the transistor level for a design containing 100 million transistors. The simulations would run so slowly that the design would be obsolete before it could be put into production.
Instead, engineers simulate functionality at the higher, more abstract levels of the hierarchy, where it is practical, but they also guarantee that each level of the hierarchy faithfully represents the next lower level. If this is done correctly, you end up building a chip that is ultimately nothing but a collection of interconnected doped regions of silicon; yet this rat's nest of interconnected regions provably gives rise to correct behavior at the highest levels of the hierarchy.
If hierarchical reductionism didn't work, neither would modern microprocessors.
We'll show you the baseball card. All you had to do was ask.
1. A high-level description of the design's functionality is written in a behavioral modeling language.
2. The high-level description is converted to an equivalent set of interconnected gates. The equivalence between the two levels can be proved formally as well as by simulating the two models side-by-side and comparing results.
3. Each gate model is shown to be equivalent to a set of switches interconnected in a particular way.
4. Each switch is shown to be equivalent to a transistor operating under certain conditions.
5. Each transistor model is shown to be an accurate representation of the behavior of a number of doped silicon regions arranged and interconnected in a certain pattern.
6. The modeled behavior of the doped silicon regions is verified by solid-state physics.
This chain of verification, through hierarchical reductionism, is what allows us to build circuits composed of hundreds of millions of transistors — and actually get them to work. Doing all of this work at the lowest level of the hierarchy would be wasteful and ultimately futile.
Hierarchical reductionism is thus not a cop-out at all, but rather an enormously useful tool for understanding and/or designing systems which are too complicated at their lowest levels to be comprehended by mere human intelligence.
Comment by keiths — January 30, 2007 @ 11:48 pm
January 31st, 2007 at 12:19 am
Hi Rock,
Interesting stuff. If you haven't read Robert Laughlin's book "A Different Universe" you might want to.
What Laughlin points out is that complex systems can incorporate both extreme sensitivity and extreme insenstivity to pertubations. These types of systems are found in engineering all the time, particularly in electronics. He uses an example of guidance systems where the amplifiers exhibit a collective instability that can create powerful amplification (by responding to small changes) but where they also include stabilizing systems that keep a plane from overcompensating.
The same can be found in biological systems. The transcription of DNA into messenger RNA is an example of collective instability that is very sensitive to pertubations whereas the translation of RNA into protein is absolutlely stable. From an intracellular and ecological standpoint this makes perfect sense. With its remarkable sensitivity, transcription can be sensitive to both the situation within the cell as well as environmental factors. But the response to that sensitivity (RNA to protein) must be absolutely insensitive.
The trick is balancing and integrating these two extremes. In engineering this is a great challenge. Is it any wonder that systems engineers stand in awe of cellular design?
Comment by Steve Petermann — January 31, 2007 @ 12:19 am
January 31st, 2007 at 12:48 am
Most machines behave reductionistically because they are deterministic rather than probabalistic. They are not self-organizing.
Holons are self-organizing wholes composed of smaller parts (which are themselves holons). Their behavior is probabilistic and not deterministic.
We do not have machines which self-assemble, which repair themselves from a wide variety of damage, or which reproduce. Reductionistic engineering is utterly incapable of building such a machine.
Comment by MatthewCromer — January 31, 2007 @ 12:48 am
January 31st, 2007 at 1:47 am
keiths, I'm talking about so called "emergent properties." As you say, each high level description in an IC can be converted to lower level descriptions, so that has nothing to do with what I'm talking about.
Comment by macht — January 31, 2007 @ 1:47 am
January 31st, 2007 at 3:09 pm
macht,
I have a post I think may be relevant to your discussion at UD. It touches on emergent phenomena and ways it can be defined formally.
Irreducible Complexity in Mathematics, Physics and Biology.
The heretical word "irreducibly complex" is even hinted to describe emergence.
Comment by Salvador T. Cordova — January 31, 2007 @ 3:09 pm
February 1st, 2007 at 5:53 pm
"In the realm of biology, it is known that life on earth is based on the DNA double
helix. But even though we understand perfectly the laws governing the interaction
of atoms, we cannot directly extrapolate these laws to explain the beginning of life,
or the auto-catalysis of complex molecular networks, or why we have brains that can
contemplate the world around us. Due to the overwhelming unlikeliness of random
events leading to complex systems like ourselves, it seems as if an organizing agent
or "God" must be invoked who puts the building blocks together."
SELF-ORGANIZATION OF COMPLEX SYSTEMS
MAYA PACZUSKI & PER BAK
IDers should understand the true purport of these ideas: God didn't do it. LOL
This is why I find Carlson & Doyle so interesting"”Even if "God didn't do it," a designer can.
Comment by Rock — February 1, 2007 @ 5:53 pm