• You are currently viewing our forum as a guest, which gives you limited access to view most discussions and access our other features. By joining our free community, you will have access to additional post topics, communicate privately with other members (PM), view blogs, respond to polls, upload content, and access many other special features. Registration is fast, simple and absolutely free, so please join our community today! Just click here to register. You should turn your Ad Blocker off for this site or certain features may not work properly. If you have any problems with the registration process or your account login, please contact us by clicking here.

Neil deGrasse Tyson on Climate Change [VIDEO]

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
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.

 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
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.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
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.
 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
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.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
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.
 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
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.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
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.


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.
 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
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.



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.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
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)


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?
 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
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.


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.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
Yeah. That was confusing. I fixed it now.




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.

And then make minuscule adjustments to the model until a perfect match is created. But if you make a minuscule adjustment to any part of the model and then move it forward in time, a new history is created which diverges farther and farther from the original. Thus the butterfly effect.

I sincerely doubt that a minuscule adjustment made on the butterfly level would have any effect on the system or that the adjustments made are of such a tiny factor.
 

ygolo

My termites win
Joined
Aug 6, 2007
Messages
5,988
And then make minuscule adjustments to the model until a perfect match is created. But if you make a minuscule adjustment to any part of the model and then move it forward in time, a new history is created which diverges farther and farther from the original. Thus the butterfly effect.

I sincerely doubt that a minuscule adjustment made on the butterfly level would have any effect on the system or that the adjustments made are of such a tiny factor.

Generally, a perfect match is considered over fitting. Besides in a test, no adjustments are made. The test has to be performed without adjusting parameters.

Well, every chaotic system is unique, but there are examples, like x:=4*x*(1-x), where a tiny change (from 0.5 to 0.51) leads to drastically different behavior.
 

Tellenbach

in dreamland
Joined
Oct 27, 2013
Messages
6,088
MBTI Type
ISTJ
Enneagram
6w5
The point is better made using elections. Cast a vote for a marxist community organizer and watch the ripples of damage spread and ruin thousands of weddings all over the globe.
 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
Generally, a perfect match is considered over fitting. Besides in a test, no adjustments are made. The test has to be performed without adjusting parameters.

Well, every chaotic system is unique, but there are examples, like x:=4*x*(1-x), where a tiny change (from 0.5 to 0.51) leads to drastically different behavior.

I'm satisfied now that Neil deGrasse Tyson was drawing on an analogy that doesn't exist in reality but is purely based on making minute adjustments to mathematical models.
 

Lateralus

New member
Joined
May 18, 2007
Messages
6,262
MBTI Type
ENTJ
Enneagram
3w4
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.
One reason? Do you have any others?

I'm amused by the Neil deGrasse Tyson hate that has bubbled to the surface recently. The guy has gone out of his way to not antagonize believers throughout his public career. When people like Richard Dawkins have blatantly attacked religious belief, Neil deGrasse Tyson has balked at that. He cares only about one thing, not letting religious belief get in the way scientific progress. You can believe whatever you want, as long as it doesn't stop you from questioning.

Watch the final 45 seconds of this video.

 

Mal12345

Permabanned
Joined
Apr 19, 2011
Messages
14,532
MBTI Type
IxTP
Enneagram
5w4
Instinctual Variant
sx/sp
One reason? Do you have any others?

I'm amused by the Neil deGrasse Tyson hate that has bubbled to the surface recently. The guy has gone out of his way to not antagonize believers throughout his public career. When people like Richard Dawkins have blatantly attacked religious belief, Neil deGrasse Tyson has balked at that. He cares only about one thing, not letting religious belief get in the way scientific progress. You can believe whatever you want, as long as it doesn't stop you from questioning.

Watch the final 45 seconds of this video.

Gravity creates tides, but what creates gravity? Bingo!
 

Haven

Blind Guardian
Joined
Apr 26, 2011
Messages
1,075
MBTI Type
ESFJ
Enneagram
2w3
Instinctual Variant
so/sp
Gravity is a force
 
Top