# Thread: Neil deGrasse Tyson on Climate Change [VIDEO]

1. ## Neil deGrasse Tyson on Climate Change [VIDEO]

Weather is chaotic, but a butterfly flapping its wings in Bali isn't going to affect the weather in Maine. That would assume that the butterfly is the initial determiner of a linear weather pattern - i.e., that weather is NON-chaotic. And that's one reason why I don't watch Neil deGrasse Tyson.﻿

2. Originally Posted by Mal12345
Weather is chaotic, but a butterfly flapping its wings in Bali isn't going to affect the weather in Maine. That would assume that the butterfly is the initial determiner of a linear weather pattern - i.e., that weather is NON-chaotic. And that's one reason why I don't watch Neil deGrasse Tyson.﻿

The word "chaos" in scientific and mathematics refers to sensitivity of time evolution of a system to initial conditions. Change a few small things, and then larger scale things can change as well later on.

Also, "linear" and "non-linear" have specific mathematical meanings in science.
See:
Linear Function -- from Wolfram MathWorld
Linear Operator -- from Wolfram MathWorld
Linear Transformation -- from Wolfram MathWorld

Notice the similarities? There is a notion of superposition that is characteristic of linearity as is the notion of homogeneity.

Chaos Theory happens to be a very large part of the study of non-linear dynamics (dynamics that are described by functions that don't follow the super position principle or homogeneity).

I'm not sure what is so controversial about what he said. Perhaps when embedded in some political debate, things take on different meaning. But the notions of linearity and chaos have been established for quite some time in science and mathematics.

3. Originally Posted by ygolo
The word "chaos" in scientific and mathematics refers to sensitivity of time evolution of a system to initial conditions. Change a few small things, and then larger scale things can change as well later on.

Also, "linear" and "non-linear" have specific mathematical meanings in science.
See:
Linear Function -- from Wolfram MathWorld
Linear Operator -- from Wolfram MathWorld
Linear Transformation -- from Wolfram MathWorld

Notice the similarities? There is a notion of superposition that is characteristic of linearity as is the notion of homogeneity.

Chaos Theory happens to be a very large part of the study of non-linear dynamics (dynamics that are described by functions that don't follow the super position principle or homogeneity).

I'm not sure what is so controversial about what he said. Perhaps when embedded in some political debate, things take on different meaning. But the notions of linearity and chaos have been established for quite some time in science and mathematics.
There is nothing political in what I'm saying. If you viewed the video, you would have seen the dog walking in a non-linear and unpredictable fashion.

Since nobody has ever, nor ever will, trace down any weather phenomenon to an initial determining factor - in fact, there is no proof that there even is an initial determiner such as a butterfly flapping its wings - Tyson is being reductionistic and dogmatic in his example of the butterfly. The very term used in this - chaos - limits the extent to which deGrasse can trace down initial causes by the very meaning of the term.

4. Originally Posted by Mal12345
There is nothing political in what I'm saying. If you viewed the video, you would have seen the dog walking in a non-linear and unpredictable fashion.

Since nobody has ever, nor ever will, trace down any weather phenomenon to an initial determining factor - in fact, there is no proof that there even is an initial determiner such as a butterfly flapping its wings - Tyson is being reductionistic and dogmatic in his example of the butterfly. The very term used in this - chaos - limits the extent to which deGrasse can trace down initial causes by the very meaning of the term.
I did watch the video. The point he is making is not about initial determinants. It is about unpredictability. The butterfly thing is a common statement people make about weather and chaos. It is meant to be a poetic illustration, not an actual statement of fact.

Consider the iterative expression:
x:=r*x*(1-x)

This dynamic is chaotic for most r values between 3.57 to 4. The starting value is of x is of great importance, but not knowing it doesn't make the dynamic not chaotic. Removing the double negative, the dynamic is chaotic, even without knowing the initial condition. The dependence of behavior on initial conditions is what makes it chaos, not the initial condition itself.

5. Originally Posted by ygolo
I did watch the video. The point he is making is not about initial determinants. It is about unpredictability. The butterfly thing is a common statement people make about weather and chaos. It is meant to be a poetic illustration, not an actual statement of fact.

Consider the iterative expression:
x=r*x*(1-x)

This dynamic is chaotic for most r values between 3.57 to 4. The starting value is of x is of great importance, but not knowing it doesn't make the dynamic not chaotic. Removing the double negative, the dynamic is chaotic, even without knowing the initial condition. The dependence of behavior on initial conditions is what makes it chaos, not the initial condition itself.
Where's the 'dynamic'? I see an equation with two variables. And you don't state whether 3.57 and 4 are included in the r values. You are saying however that not knowing the value of x does not make the "dynamic" non-chaotic. I'm saying that deGrasse claims to know that there has to be a "value," when in fact nobody knows whether or not there is an x-value to begin with.

Yes I know what Tyson was saying, the dog's behavior is unpredictable as the weather. and I also know he's repeating an old saw about a butterfly influencing - no, creating - a weather pattern.

6. Originally Posted by Mal12345
Where's the 'dynamic'? I see an equation with two variables. And you don't state whether 3.57 and 4 are included in the r values. You are saying however that not knowing the value of x does not make the "dynamic" non-chaotic. I'm saying that deGrasse claims to know that there has to be a "value," when in fact nobody knows whether or not there is an x-value to begin with.

Yes I know what Tyson was saying, the dog's behavior is unpredictable as the weather. and I also know he's repeating an old saw about a butterfly influencing - no, creating - a weather pattern.
At this point, I am not sure what the disagreement is.

"Dynamic" is short for "dynamical system". The equation I gave is one such example, and was explicitly chosen to be simple. If r=4, you would have an almost perfect random number generator, on notable exception is when x=0.5. There are r values from a little above 3.57 till 4 that exhibit chaotic behavior (that is, sensitivity to initial conditions).

As far as values and such, math is taken to be a description of a real system. The equations governing weather are quite complicated. But things like barometric pressure, temperature, wind speed, and so on are measurable quantities. Measurements are what is taken to be "x". A butterfly can change very small portions of things like pressure, and the speed of air movements. These minuscule changes in a chaotic dynamical system could lead to very large scale changes. That is all there is to "the butterfly effect". I realize it's a bombastic statement in some sense. But he isn't claiming that some particular butterfly somewhere caused hurricane Sandy in particular, or anything of the sort.

Again, I am just trying to find out what you disagree with, since statements like the ones Tyson made seem quite uncontroversial on their own.

7. Originally Posted by ygolo
At this point, I am not sure what the disagreement is.

"Dynamic" is short for "dynamical system". The equation I gave is one such example, and was explicitly chosen to be simple. If r=4, you would have an almost perfect random number generator, on notable exception is when x=0.5. There are r values from a little above 3.57 till 4 that exhibit chaotic behavior (that is, sensitivity to initial conditions).
Apparently I haven't studied this math, because when I plug 4 in for r, x resolves to 3/4. I'm assuming the * is multiplication and that you didn't include any powers.

Originally Posted by ygolo
As far as values and such, math is taken to be a description of a real system. The equations governing weather are quite complicated. But things like barometric pressure, temperature, wind speed, and so on are measurable quantities. Measurements are what is taken to be "x". A butterfly can change very small portions of things like pressure, and the speed of air movements. These minuscule changes in a chaotic dynamical system could lead to very large scale changes. That is all there is to "the butterfly effect". I realize it's a bombastic statement in some sense. But he isn't claiming that some particular butterfly somewhere caused hurricane Sandy in particular, or anything of the sort.

Again, I am just trying to find out what you disagree with, since statements like the ones Tyson made seem quite uncontroversial on their own.
Many uncontroversial theories are unfalsifiable. I'm saying it's false until proven otherwise.

8. Originally Posted by Mal12345
Apparently I haven't studied this math, because when I plug 4 in for r, x resolves to 3/4. I'm assuming the * is multiplication and that you didn't include any powers.
It will depend on your starting value of x. It is important that this is iteration. x_(t+1)=4*x_t*(1-x_t). I can see the source of the confusion. Think of it like programming x:=4*x*(1-x).

If you start with x=0.5. 4*x(1-x)=4*0.5(1-0.5)=4*0.5*0.5=1. If we iterate again, 4*x*(1-x)=4*1*(1-1)=0. Iterating again, 4*x*(1-x)=4*0*(1-0)=0. Leaving it stuck at 0.
If you start with x=0.51. 4*x(1-x)=4*0.51(1-0.51)=4*0.51*0.49=0.9996. Iterate again, we get 0.00159936, then 0.006387208, then 0.025385647, then 0.098964864, then 0.356683278, then 0.917841269, a very different time evolution of the x value.

Originally Posted by Mal12345
Many uncontroversial theories are unfalsifiable. I'm saying it's false until proven otherwise.
Chaos theory is a mathematical description. One cool thing about it is that it is much easier to "retrodict" (infer the past from the present) than to predict (infer the future from the present). Both these notions come from the fact that the time evolution of the variables diverge as we go forward in time (and so converge when you go back). Retrodictions from a chaotic dynamical model can be tested. Hence chaotic models are falsifiable.

9. Originally Posted by ygolo
It will depend on your starting value of x. It is important that this is iteration. x_(t+1)=4*x_t*(1-x_t). I can see the source of the confusion. Think of it like programming x:=4*x*(1-x).

If you start with x=0.5. 4*x(1-x)=4*0.5(1-0.5)=4*0.5*0.5=1. If we iterate again, 4*x*(1-x)=4*1*(1-1)=0. Iterating again, 4*x*(1-x)=4*0*(1-0)=0. Leaving it stuck at 0.
If you start with x=0.51. 4*x(1-x)=4*0.51(1-0.51)=4*0.51*0.49=0.9996. Iterate again, we get 0.00159936, then 0.006387208, then 0.025385647, then 0.098964864, then 0.356683278, then 0.917841269, a very different time evolution of the x value.

That clarifies a lot. Because you originally gave us x=r*x*(1-x), and not x:=r*x*(1-x)

Originally Posted by ygolo
Chaos theory is a mathematical description. One cool thing about it is that it is much easier to "retrodict" (infer the past from the present) than to predict (infer the future from the present). Both these notions come from the fact that the time evolution of the variables diverge as we go forward in time (and so converge when you go back). Retrodictions from a chaotic dynamical model can be tested. Hence chaotic models are falsifiable.
How are they tested?

10. Originally Posted by Mal12345
That clarifies a lot. Because you originally gave us x=r*x*(1-x), and not x:=r*x*(1-x)
Yeah. That was confusing. I fixed it now.

Originally Posted by Mal12345
How are they tested?
Essentially, you run the model backwards in time based on a short amount of near-term data, and then check against past data. It's not easy by any means, because multiple histories still lead to the same place in many dynamical systems. Nevertheless, in areas where trajectories diverge when running forward in time, they will converge when the go back in time.

It is still just comparing models to measurements.

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