I must admit confusion. A theory that tells us things are "unpredictable" as the narrator states. What is this a theory of? What is being understood within the chaos Thai? I do not get the connection with fractals and self similarity. It would seem to be the opposite of this.
Chaos is a form of symmetry so when it breaks, fractals are formed.
And remember, fractals are scale invariant meaning that no matter how much you fractals them, they still look the same. In physics this means the laws of nature apply exactly the same to all pats of them on all scales from the smallest to the largest.
They occur at phase transitions
You (and I), indeed all of life, are a form of energy which exists only in phase transitions.
It is the reasons you see all the impossible irreconcilable paradoxes in your life that you see.
It will always be this way for all human beings unless we change to a new form of matter.
The problem with this is things like thought would be impossible in a non-chaotic form of matter.
If we want life, we are trapped with all the impossibilities of it
"A system in a state of total disorder is more symmetric than a system with some order to it"
Don't you mean more "uniform" as apposed to "symmetric"? A system in complete chaos would be uniform across the system but I do not see how it is symmetric?
When you say there is symmetry it sounds like what you are describing is that there is chaos throughout the system as a whole. Symmetry to me means you can take a slice from anywhere and it looks the same regardless. This is not true in chaos. You are just saying there is no order throughout the system which gives it uniformity in its disorderlyness but not "symmetry".
I think we are having one of those "whose of first discussions"
As I think of symmetry (and I freely admit I could be wrong), symmetry is something that is invariant.
FYI- I'm relatively new to the concept of symmetry as it relates to other areas of physics as it was only recently introduced to to me by another blogger who used to be on this site who called himself Street Dog (he is an ophthalmologist who studied at Cal Tech as an undergrad) and was curious to understand a little more about my fractal fetish.
Anyway, as I understand it, total randomness which has been translated or rotated or inverted still remains total randomness and is therefore still symmetric relative to itself.
Further, if you think of symmetry as a form of indistinguishably, you could not tell a chaotic 1 meter cloud of gaseous molecules from another 1 meter cloud no matter how hard you tried.
But once a pattern were introduced into the 1 meter cloud of molecules- like a swirl in cloud not in the other- the symmetry of the two clouds would be broken and you could tell the two clouds apart if you tried.
It makes sense but it does not sound like "symmetry" to me. I see where you are going with the randomness and the inability to distinguish one from another unless they are placed on top of one another but this just strikes me as random complexity not symmetry. To me symmetry means structural sameness not just that the systems are both grossly random. I will read the link.
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I must admit confusion. A theory that tells us things are "unpredictable" as the narrator states. What is this a theory of? What is being understood within the chaos Thai? I do not get the connection with fractals and self similarity. It would seem to be the opposite of this.
The best analogy I can share is that fractals are the constant part of the chaos.
Think of them as the N dimensional constants in the N dimensional equation.
There is both stasis and change simultaneously in a chaotic system.
Fractals are the stasis
Are fractals only apparent then when the chaos breaks?
I think so , "yes"
Chaos is a form of symmetry so when it breaks, fractals are formed.
And remember, fractals are scale invariant meaning that no matter how much you fractals them, they still look the same. In physics this means the laws of nature apply exactly the same to all pats of them on all scales from the smallest to the largest.
They occur at phase transitions
You (and I), indeed all of life, are a form of energy which exists only in phase transitions.
It is the reasons you see all the impossible irreconcilable paradoxes in your life that you see.
It will always be this way for all human beings unless we change to a new form of matter.
The problem with this is things like thought would be impossible in a non-chaotic form of matter.
If we want life, we are trapped with all the impossibilities of it
Deb, your daughter has a headache. It is severe and but I can treat the pain easily.
What I also want is to predict the headache does not represent anything seriously harmful or debilitating to her.
Prediction is a very significant issue
Deb, you have always misunderstood my faith in science.
So is chaos symmetry we can just not see because chaos would seem to be the exact opposite of symmetry. Where is the symmetry in chaos Thai?
Chaos is more symmetric
A system in a state of total disorder is more symmetric than a system with some order to it
"A system in a state of total disorder is more symmetric than a system with some order to it"
Don't you mean more "uniform" as apposed to "symmetric"? A system in complete chaos would be uniform across the system but I do not see how it is symmetric?
Are we playing "Who's on first"?
Yes
A state of total randomness is relatively symmetric with itself.
no matter how you rotate or shift or translate a random state, it will still look random.
Break the randomness and add something which is not random and this will not be symmetric with itself
I guess I am stuck on semantics as I see this a uniformity and not at all symmetry
Uniformity of what?
Uniformity of the space as being non-uniform.
When you say there is symmetry it sounds like what you are describing is that there is chaos throughout the system as a whole. Symmetry to me means you can take a slice from anywhere and it looks the same regardless. This is not true in chaos. You are just saying there is no order throughout the system which gives it uniformity in its disorderlyness but not "symmetry".
Two slices show equal disorder but they are not a mirror of one another hence "symmetrical".
Sorry, I've been working a lot of late
I think we are having one of those "whose of first discussions"
As I think of symmetry (and I freely admit I could be wrong), symmetry is something that is invariant.
FYI- I'm relatively new to the concept of symmetry as it relates to other areas of physics as it was only recently introduced to to me by another blogger who used to be on this site who called himself Street Dog (he is an ophthalmologist who studied at Cal Tech as an undergrad) and was curious to understand a little more about my fractal fetish.
Anyway, as I understand it, total randomness which has been translated or rotated or inverted still remains total randomness and is therefore still symmetric relative to itself.
Further, if you think of symmetry as a form of indistinguishably, you could not tell a chaotic 1 meter cloud of gaseous molecules from another 1 meter cloud no matter how hard you tried.
But once a pattern were introduced into the 1 meter cloud of molecules- like a swirl in cloud not in the other- the symmetry of the two clouds would be broken and you could tell the two clouds apart if you tried.
Does this make sense?
I meant to include the following link
It makes sense but it does not sound like "symmetry" to me. I see where you are going with the randomness and the inability to distinguish one from another unless they are placed on top of one another but this just strikes me as random complexity not symmetry. To me symmetry means structural sameness not just that the systems are both grossly random. I will read the link.
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