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 NONchaotic. And that's one reason why I don't watch Neil deGrasse Tyson.
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06082014, 09:18 AM #1
Neil deGrasse Tyson on Climate Change [VIDEO]
"Everyone has a plan till they get punched in the mouth." Mike Tyson
“Culture?” says Paul McCartney. “This isn't culture. It's just a good laugh.”

06082014, 01:52 PM #2
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 "nonlinear" 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 nonlinear 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.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

06082014, 02:48 PM #3
There is nothing political in what I'm saying. If you viewed the video, you would have seen the dog walking in a nonlinear 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."Everyone has a plan till they get punched in the mouth." Mike Tyson
“Culture?” says Paul McCartney. “This isn't culture. It's just a good laugh.”

06082014, 03:12 PM #4
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*(1x)
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.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

06082014, 04:19 PM #5
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" nonchaotic. 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 xvalue 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."Everyone has a plan till they get punched in the mouth." Mike Tyson
“Culture?” says Paul McCartney. “This isn't culture. It's just a good laugh.”

06082014, 04:48 PM #6
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.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

06082014, 05:13 PM #7
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.
Many uncontroversial theories are unfalsifiable. I'm saying it's false until proven otherwise."Everyone has a plan till they get punched in the mouth." Mike Tyson
“Culture?” says Paul McCartney. “This isn't culture. It's just a good laugh.”

06082014, 05:37 PM #8
It will depend on your starting value of x. It is important that this is iteration. x_(t+1)=4*x_t*(1x_t). I can see the source of the confusion. Think of it like programming x:=4*x*(1x).
If you start with x=0.5. 4*x(1x)=4*0.5(10.5)=4*0.5*0.5=1. If we iterate again, 4*x*(1x)=4*1*(11)=0. Iterating again, 4*x*(1x)=4*0*(10)=0. Leaving it stuck at 0.
If you start with x=0.51. 4*x(1x)=4*0.51(10.51)=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.
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.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

06082014, 06:18 PM #9"Everyone has a plan till they get punched in the mouth." Mike Tyson
“Culture?” says Paul McCartney. “This isn't culture. It's just a good laugh.”

06082014, 06:23 PM #10
Yeah. That was confusing. I fixed it now.
Essentially, you run the model backwards in time based on a short amount of nearterm 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.
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
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