Tuesday, March 22, 2011

A Return To The Invisible College 3

Is reductionistic thinking in science coming to an end?  Will the entire community turn to seeing complex systems and all they can contribute to scientific studies?

In this part of this series we will discuss the major problems in reductionism and the future of complex systems studies.

Hubel Weisel's Cat Experiment And The Search For The Grandmother Neuron
David Hubel and Torsten Wiesel conducted the most important work in neurobiology between 1960-1975.  The attempt was traditional for the time, it was an attempt to formulate a simple point for point reductive structure between stimuli and neuron reaction. You can see the part of a video about it here: http://youtu.be/IOHayh06LJ4.  The goal was the normal reductionist goal - to know the starting state of a neuron and to be able to predict it's reaction 100%.  This view has since been rejected in favor of neural networks.  One study in support of this old theory was done by Rodrigo Quiroga from the University of Leicester, UK.  His research published in Nature Magazine (vol 435, p 1102) in 2005 seemed to find evidence for these grandmother cells.  They are called grandmother cells because the idea is that they are programmed to recognize important people, animals or things such as one's grandmother.  But this paper has been criticized.  As Carl Zimmer explained well:
One of the biggest objections to the idea of grandmother cells is a matter of math: If every recognizable part of our vivid perception of life is detected by a grandmother cell, there don’t seem to be enough neurons in the brain to handle the job. Skeptics also point out that neurons responding strongly to one particular person or place often turn out to respond (albeit more weakly) to another stimulus as well. For example, in Quiroga’s study some neurons that responded strongly to Jennifer Aniston also responded to Lisa Kudrow, Aniston’s costar on Friends. Grandmother cells are supposed to respond to only one thing, yet these neurons seem to be reacting to a range of things.
The paper specifically stated that it did not respond to Julia Roberts, Brad Pitt, etc.  They also discovered that this neuron would also respond the a picture of the Sydney Opera House.  Thus there are only a few cases of sparse coding or grandmother neurons.  Yet the vast number of attempts to find grandmother neurons failed.  Why?  Each layer of neurons would need to expand exponentially, and there would not be enough neurons in the brain to recognize shapes in a reductive structure.  This research was rejected in favor of neural networks.

Even Quiroga does not think that he has found the "grandmother cell."  According to Carl Zimmer again Quiroga "...suspects that a very sparse network of neurons - perhaps out of the billions in our heads - can develop this kind of response to an individual."

click to enlarge
random network vs scale-free network
Some of the most important systems in the body are bifurcating systems.  When it is said that these systems are "scale free," it means that no matter, whether they are large in size or on molecular in size, they exhibit the same tendencies and shapes.  But there is more.  It is the structure of these scale free networks that are different.  As Jan Matlis has put it,
...the nodes of a scale-free network aren't randomly or evenly connected. Scale-free networks include many "very connected" nodes, hubs of connectivity that shape the way the network operates. The ratio of very connected nodes to the number of nodes in the rest of the network remains constant as the network changes in size.
These bifurcating systems can best be understood by looking at as neural networks rather and individual components.   A bifurcating system is a biological network in which a small change at the starting point of a process can lead to radical and unexpected changes in the outcome of the process.  reductionist approach cannot describe this process because there are no direct one on one cause and effect components.  These bifurcating systems resemble a tree structure and are called dendritic.  A reductionist approach would view all the bifurcations as being determined by a specific gene in the genome.  The problem is that there are not enough genes in the human genome to be able to account for all these bifurcations!  

Chaotic Systems (non-linear, non-addiditive)
Interesting complex biological systems are not understandable through reductionist techniques.  Reductionist approaches are good for simple systems in breaking down their component parts, but cannot understand the whole system's overall operation.  In these systems, chance interaction can change the final outcomes dramatically.  In Chaotic systems you have strange attractors around which the chaotic system "hovers."
In chaotic systems there is no absolute pure answer out there.  The area around the strange attractor is the very phenomena of chaotic systems.  Thus in Biology for example, most of the interesting systems and phenomena are chaotic, thus rendering the last 500 years of reductive science of little effect in understanding these phenomena.

Two different kinds of determinism
Periodic Determinism (just add one factor each time) Reductionist - is a point for point, one for one, cause and effect relationship where if you know the starting point, you can calculate the ending point.  Periodic systems have attractors that will bring back the system to themselves (the attractors being the pure perfect system and how it works).
Aperiodic Determinism (you cannot see repeating patterns you have to go stepwise and apply the rule over and over again) things at happened at irregular intervals which cannot be predicted, thus producing final outcomes which are equally unpredictable.

A water wheel exemplifies both a steady state periodic reductionistic state AND a chaotic non-linear system.  It can be a simple one component periodic steady state or two component periodic steady states, or even up to four components steady state periodic system.   The system can be as complex as it needs to be and still a be steady state periodic system.    But somewhere in the doubling process, it becomes a non-linear periodic system achieving a chaotic pattern (a never repeating pattern, infinitely different along the way).  Here is the classic water wheel which will demonstrate the random, unpredictable motions that occur in the water wheel after a period of time.  If you cannot see the embedded video here is the link: http://youtu.be/HH2jPq9g6CI.

James Yorke said that as soon as the pattern repeats to on an odd number, a chaotic tipping point has been reached.  Here is an interview of Malcolm Gladwell author of the book entitled The Tipping Point.  If you cannot see the embedded video here is the link: http://youtu.be/QHxf68nb_-o.

In the past before the discovery of chaotic theory, chaotic behavior was discounted as noise or as problems with the system, measurements, or anomalies.

Second generation chaotic studies focused on the fact that even though there appeared to be repetitions in the patterns they were not precisely the same.  These minute differences get magnified over the entire length of the system producing dramatically different effects on the cycle.  This is the butterfly effect.  Wich chaotic systems the closer you look the same amount of noise will exist.  It is a scale free system, not affected by size.  The variables still exist.

Is a complex pattern, or formula that produces itself scale free. Information that codes for a pattern i.e., like a line where the line moves around with such an infinite amount of complexity in a finite space.  A two dimensional object a fracture of a dimension.  IT is 1.3 dimension.  It has fractional dimension to it.

Another definition is that the amount of variability is the same regardless of the scale of it.  There is no noise in it.

Fractal genes are genes with instructions independent of scale.  This is an excellent lecture given by the Biologist Robert Sapolsky, professor of Neurology and Neurological Sciences at Stanford University.

"As soon as you have 60-65 different identifiable entities interacting together, the combinations exceed all of the elementary particles of the Universe."
Robert Ulanowicz
Robert Ulanowicz
Emergent Complexity
A simple definition of emergence "...is the way complex systems and patterns arise out of the multiplicity of relatively simple interactions."  This means that the whole is not just the sum of its parts.  New qualities emerge when things get to a certain level complexity.  Emergence is about relationships and connections between things, entities or systems.

An interesting conversation was found in YouTube concerning emergence.  The initial comment was made by a user named ren5311.  He stated about emergence, "Now, on the evidence,  Name one emergent property.  That is, name one property known to be more than the sum of individual parts.  Emergence and complexity are confused."  To this question another user named SisphusRedeemed stated, I'll name three; solidity, liquidity and gaseousness.  No single molecule of water is 'liquid' nor it is 'sold' nor 'gaseous.'  Liquid, solid and gas only emerge when you get a collection of molecules together.  If you look at only one molecule, you'll never be able to predict what phase it's in.  But at the same time, the liquid, solid or gaseous water is nothing more than a collection of those molecules.  Hence, these properties are emergent."

If you cannot see the embedded video here is the link: http://youtu.be/gdQgoNitl1g.

If you cannot see the embedded video here is the link: http://youtu.be/S5NRNG1r_jI.

In the last installment of this series, we will discuss where science could head in order to breakthrough the barriers and chaotic systems pose.


Anonymous said...

Thanks for some quality points there. I am kind of new to online , so I printed this off to put in my file, any better way to go about keeping track of it then printing?

Anonymous said...

Thanks for some quality points there. I am kind of new to online , so I printed this off to put in my file, any better way to go about keeping track of it then printing?

Phyllis Janes said...

I like Malcolm Gladwell's way of thinking.  He finds different perspectives in the most common things.

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