Rob: Okay I want to keep moving along because we're going to run out of time soon. You mentioned in the first part of the interview and you talk about how a central characteristic of the systems view of life is nonlinearity, which complexity theory is based on -
FC: Right.
Rob: - you said all living systems are complex, in other words nonlinear networks. Could you just explain a bit about nonlinear?
FC: Yeah, well you see when you - the way you mention this is I think the best way of introducing readers or listeners to this idea of complexity that once you realize that life is networks, that all living systems are organized in terms of networks, then you know that a network is a pattern of relationships and it's a nonlinear pattern of relationships. Already, before going to networks we can talk about cycles which are also an important property of all living systems. We have ecological cycles, we have in our bodies the blood cycles and so does the lymphoid and we have you know brainwaves. We have all kinds of nonlinear patterns, but -
Rob: What is nonlinear mean?
FC: Well, linear is in - well there are actually two meanings, it's good that you ask that. In terms of geometry, it's a straight line and so anything that is not a straight line, anything that is a curve is nonlinear, and especially a circle or cycle is nonlinear and a network is nonlinear because a network goes in all directions, not just in one straight line. And in mathematics, linear equations, and here we'll have to get a little bit technical. Equations where the variables appear in the first power. So, for instance the - very simple if you have an equation you know Y equals two X, the variables are these letters Y and X, that's a linear equation. If you have an equation Y equals X square or X to the power of five, that's a nonlinear equation. Now the nonlinear equations we're dealing with when we describe living systems of course far more complex, they are differential equations, which means they use differential calculus and higher mathematics. And in fact in the book, in the chapter on complexity theory, I go into some of these details and I explain -
Rob: Yes, great detail.
FC: - linearity and nonlinearity in more detail.
Rob: You know I want to nail down one thing and that is this aspect of the nonlinear nature of life, of network systems. It's the core point that forces us to reject a mechanistic model of science because that model totally sails to address those dimensions of life and subatomic particles, and things like that.
FC: Yes, for instance when you think of a very simple machine, think of a bicycle, alright? So a bicycle has a linear chain of cause and effect. When I push the pedals of a bicycle, this motion, this force is transferred through the chain to wheels and maybe gears and finally to the wheels of the bicycle and through the friction with the ground, the bicycle is pushed forward. So, this is all a linear chain of cause and effect, but in living systems when you influence a living system, the effect goes around in circles and they're so called feedback loops which means that things come back to you. So whatever we put out in the environment, eventually will come back to us and so we say we build cars and factories that use fossil fuels and they emit greenhouse gases that change the atmosphere and that increase the energy in the atmosphere which then has many consequences like droughts, like hurricanes, like forest fires, the melting of glaciers and so on, very severe consequences of climate change; which is a feedback of our actions, of our human actions. And that is because the whole planet gaia is a living system and it is a nonlinear system. And it is well known today that to model these linear systems is exceedingly difficult to construct mathematical models of climate change is highly complex and very difficult.
Rob: And virtually impossible using mechanistic science.
FC: Right.
Rob: So, let's go a little bit further into this and let's talk about chaos theory where you talk and discuss strange attractors and bifurcation points and fractals, how do they fit in?
FC: Well, the nonlinear mathematics that was developed in the 1970s and 1980s with the help of computers is really a mathematics of relationships and patterns, which is critical when you deal with nonlinear systems. And the central task was how to solve nonlinear equations, and mathematicians and scientists developed certain techniques based on computers which solved equations, essentially by trial and error. Let me say that when you a mathematical equation, and our listeners will remember this from school, that you have a mathematical equation and you manipulate it, and there're certain techniques and certain rules how you can manipulate an equation. You know you move things from left to right and from right to left, you multiply everything by five or whatever, and there're certain techniques and at the end you have a formula. And that's the solution of the equation is the formula. Now, nonlinear equations you cannot solve in this way. You cannot manipulate them until you get a formula as a result. What you have to do is you solve them by trial and error. You assume that the variables have certain values and you try it out and if it doesn't work, you try something else. And there are again certain tricks and certain rules where you can do that. And that - this is called solving an equation numerically. And these techniques existed long before computers, but you can imagine solving an equation by trial and error takes a lot of time and a lot of patience. And so what happened with computers that the time was reduced dramatically and where you had to work for two months to solve an equation by hand, by trial and error, you could do it now in a few minutes or even in a few seconds. And so, this was a huge advance that computers brought us and the solution is not an equation, but is a pattern and that's the crucial point here. A geometric shape, a pattern which represents the dynamics of the system, the way the system behaves, and these patterns are called attractors. And there are certain attractors called strange attractors that describe chaotic systems which are systems that don't have regularities, that are sort of random, and then there are other attractors like point attractors or periodic attractors that describe periodic systems. So, this is the relationship attractors are geometric patterns that describe the dynamics of the whole system.
Rob: And bifurcation points?
FC: And bifurcation points are - well, these strange attractors can be stable or can be unstable. When they are stable, that means the system behaves in the same way and continues to behave in that way. When they're unstable it means that a totally new behavior can emerge and that is called a bifurcation because the system branches off into a new behavior and a new branch of the attractor. And this is to me one of the most important results of complexity theory, the discovery of emergence. That there can be a spontaneous emergence of new forms of order.
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