consciousness precedes real time

[scruffy]

Why should anyone take you seriously after reacting "I don't have time for any bullshit today" when someone proves to you that chaotic systems are deterministic when you insisted they were not?

You didn't prove anything.

You're making a bogus claim.

One that you can disprove for yourself, if only you'd be a careful observer.

that's a huge misunderstanding on your part and shows you can't admit error like an adult.

There is no error.

I'd like an answer please, you make lofty claims here regularly to the point of insinuating you are a superior intellect, so please explain why you can't simply say "OK I was wrong to say that, what I meant was..." or something like that?

Being wrong and admitting it earns respect, being wrong and berating someone who points that out to you makes you look like an arrogant blowhard.

Go look at the Lorenz attractor CAREFULLY and tell me what you see

 

[Sherlock Holmes]

You didn't prove anything.

You're making a bogus claim.

One that you can disprove for yourself, if only you'd be a careful observer.

I am not making the claim, mathematicians are, should I reject them and listen to you instead?

Don't you see how idiotic you look saying I made a bogus claim? I said chaos is deterministic and anyone who understand this knows that.

You are either out of your depth or very bad at explaining what it is you believe.

Go look at the Lorenz attractor CAREFULLY and tell me what you see

I see that it's deterministic:

So that clears it up I think, did you say you actually get paid for doing what you do?

Tell me how can deterministic equations generate random results? perhaps you have a bug in your modelling code, ever heard of GIGO?

Perhaps you're getting confused between chaos and pseudo-randomness, who knows, you're all over the place.

 

[scruffy]

I am not making the claim, mathematicians are, should I reject them and listen to you instead?

Don't you see how idiotic you look saying I made a bogus claim? I said chaos is deterministic and anyone who understand this knows that.

You are either out of your depth or very bad at explaining what it is you believe.



I see that it's deterministic:

View attachment 1000841

So that clears it up I think, did you say you actually get paid for doing what you do?

Tell me how can deterministic equations generate random results? perhaps you have a bug in your modelling code, ever heard of GIGO?

Perhaps you're getting confused between chaos and pseudo-randomness, who knows, you're all over the place.

Do what I tell you.

Don't believe CNN, that's just stupid.

Go look at it with YOUR OWN EYES and tell me what you see.

Don't be a fallacious authoritarian.

Go look at the Lorenz attractor, then get back to me.

 

[scruffy]

Here, I will give you a quick course on chaos and randomness

First of all, let's start here. Here is the Lorenz attractor

Animating the Lorenz Equations

I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck. The equations are: $\begin{align*} \dot{x} &= \sigma(y-x)...

mathematica.stackexchange.com

Now, look at the pretty picture, and tell me what you see with your own eyes.

You see the attractor changing shape, amirite?

To understand what this means, we will have to take a little trip.

Let us first understand that the Lorenz system is nonlinear snd the equations are static. Nevertheless it is a fractal (fractional) attractor with a Hausdorff dimension of just over 2.

It turns out we can REPLACE this system (map it) with stochastic differential equations with the same dimensionality. Why do this? Because it gives us MEASURES.

What this means in practice is we are replacing the random motion of particles entering the vortex, with random motions of the vortex itself.

Start here, to understand why we want to do this:

Random dynamical system - Wikipedia

en.wikipedia.org

Scroll down to where it says Motivation 2, and the look just below where it says "Example". Read carefully.

We are substituting deterministic transition matrices with Markov matrices, and we can do this because there is a topological mapping from one to the other. Now keep reading where it says "formal definition". Note the verbiage about MEASURE PRESERVING TRANSFORMATIONS. That's why we can do this, because we're preserving the measure between the stochastic metric and the deterministic nonlinear metric.

From a topological standpoint, the two are one and the same. The formal treatment is given by the subsets of omega-limit sets in the phase space. The Lorenz attractor, it turns out, is not one trajectory, instead it is an infinite complex of surfaces with zero volume and infinite surface area.

You will notice in the simulation, that several times the attractor does a "reset", it's shape becomes discontinuous over a brief interval of time. This is exactly the same thing that happens in the financial markets, where stochastic differential equations are also used to map nonlinear systems. This:

looks exactly like the motion of a particle in a Lorenz vortex it is stochastic and also nonlinear, some would say it is random "and" chaotic but the truth is the two can not be divorced.

The key issue is SCALE. As you know from studying fractals, measured lengths change with the yardstick, and therefore areas and volumes change and so do dimensions. It is perfectly accurate to say a weather system is random, at the level of particles that enter the vortex - even though the global dynamic retains its shape - just as it is accurate to say the roll of dice is random, even though if you're being a stickler you could argue that it's a deterministic system that merely magnifies the initial conditions. The OUTCOME is random, just as the position of a particle in a Lorenz vortex is random. It can NOT be predicted in advance (I defy you to try lol).

It is most USEFUL to treat this as a stochastic system, this way you can write differential equations that will take you to the shape a lot faster than plotting points.

Since I don't have a math font I can't show you the topology. But you can find it if you look around a bit, and I can verbalize it. Attractors are the omega limits of nonempty inward sets Z in X such that dF^n(X,Z) < epsilon for every n. The "d" is why the differential form is useful, it stands for distance (not derivative), which is the MEASURE we started with. With stochastic differential equations you have a complete set of measures within the given dimensionality, limited only by the Hausdorff properties (like, the area of a line is zero).

Measure theory SOUNDS simple but it's not.

Hausdorff measure - Wikipedia

en.wikipedia.org

We call the outcome of a roll of dice "random" because that's how we perceive it, and that's how we measure it. Whether it is or is not truly random is completely beside the point. The only USEFUL way to treat it is as a random variable.