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Can the Limit concept from Calculus be used to predict chaotic systems, like ImAFungi said?
The supposed tipping point/breaking point that creates chaos should then be viewed to be of a higher order, not less order, nor more chaotic.
You cannot have x, y, z without having all 3 dimensions.
reply to post by ImaFungi
Irrational numbers are infinitely long, so the next digit is never known. That is at least one kind of true randomness.
The first time anyway.
i think it is more likely that the universe is primarily composed of chaotic order, and that any object which is explicitly ordered and deterministic (such as is the case with information), is necessarily artificial or unnatural.
you have mentioned a type of spectrum of well-orderedness which is certainly necessary. for example, if i say that the orbit of the earth around the sun is not deterministic, someone will come up in here citing all kinds of relativistic formulations claiming i am full of it. nevertheless, such an orbit is the quintessential example of a chaotic system: one which is topologically mixing (can be perturbed by unpredictable events) (#2), and one which tends to revisit the neighborhood of all previous orbits (#3).
The issue of determinabilty isnt about me or it, it is about truth. But yes I think I just had some thoughts that allow me to agree with you... if the algorithm uses probability I guess it is not determinable, but I still find it hard to break away from my instinct. What made me potentially admit maybe understand what your saying, is thinking of lottery balls, (similar to mentioning guessing a random number) you know the lottery ball machines that pop up the balls, forget playing the lottery, if you were standing in front of one of the machines, and it had 1000 numbered balls in it, and you had to guess the order the balls would pop up, it would not be likely you would correctly determine. But I am still urged to say it is still based off of laws of physics, and if you had all the information about every ball, and pico second to pico second updates as to where each ball was, and all physical variables like the angular momentum and velocity and momentum and saw each ball bouncing off each other and their positions, and then was notified when the vacuum thing was turned on or however that happens, if you had all that information, and could sort through it frame by frame, as if it was occurring in slow motion, you should be able to determine every ball to come up, if you knew all the laws of physics. Does this not at all relate to an algorithm that may utilize randomness or probability, it is still limited to a grid, it is still operating under limitations and rules, there is a limited amount of things it may do step by step. So I feel like given all the information, it should be predictable.
the cellular automaton appears to be predictable to you. that is because you are occupying a different, perpendicular, dimension of observation upon the system than the system is capable of occupying upon itself.
in other words, the system is not aware of the fact that it is producing larger and smaller triangles. the algorithm rule set which generates the pattern simply plugs away at it, one pixel at a time. the algorithm doesent care about what came before or is about to happen. it just goes and goes.
so, while it appears to be deterministic to you, that is because you are observing the STATE (am i over-stressing the importance of this word? no.) of the system, outside of the relative time domain of the system itself. you do not occupy the same time frame. you are "above" it.
I dont agree with your sentiments, you are saying objective reality does not exist until through our subjectivity we objectify our minds, we make our minds equal to objectivity and that is when objectivity exists.
but none of what i have said in this post relates to the question of predictability. it is possible to predict the sequence of generated terms in the automaton only by explicit calculation of each and every term. again, this is maximum entropy. equivalent to random. like unto the sequence of digits for the number PI.
PI has been calculated out to the bajillionth term. so, what is the bajillion-and-oneth term? there is only one way (that we know of) to answer this: generate the next term explicitly. this is maximum entropy. equivalent to random.
i can hear you thinking that surely PI must have some sort of predetermined and definitive order, and that whether or not we are aware of its order, the order nevertheless exists. that may be true. but that is not the point. the number PI could be speaking mandarin chinese, but if we are personally not aware of the language it is speaking, it is functionally equivalent to random.
on the other hand, if we were suddenly to become aware of the ordering principle of PI, the amount of entropy it contains would drop significantly. interestingly, the 2nd law of thermodynamics says that a lowering of entropy is not possible.... within a closed system. in the moment that we discover the ordering principle, we become part of the system of PI, changing it from a closed to an open system and allowing the lowering of entropy to take place.
i am sorry if that is more than you asked for.
the diffraction patterns of crystals say otherwise. this is how the 3D helix structure of DNA was deduced: by studying its 2D diffraction pattern which implicitly contains information about its symmetry in three dimensions.
Also, must irrational numbers continue to infinity? Couldn't the answer be complete at any decimal place?
FIXED: Information is an exchange (and the carrier/symbol-set) - between one physical (mental) system to another.
a STATE can be translated into information, and can even generate information. but the state does not exist in a linearized dimension: it is a total unified thing which is as though all of the information were being 'transmitted' all at once.
If the universe is 3 dimensional spatially, which it appears to be, then how can any 2d object truly exist? It cant have a quantitative value of length and width and a value of 0 for depth
The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information "inscribed" on the surface of its boundary.
Demonic device converts information to energy
The laws of physics say that you can't get energy for nothing — worse still, you will always get out of a system less energy than you put in. But a nanoscale experiment inspired by a nineteenth-century paradox that seemed to break those laws now shows that you can generate energy from information.
Masaki Sano, a physicist at the University of Tokyo, and his colleagues have demonstrated that a bead can be coaxed up a 'spiral staircase' without any energy being directly transferred to the bead to push it upwards. Instead, it is persuaded along its route by a series of judiciously timed decisions to change the height of the 'steps' around it, based on information about the bead's position. In this sense, "information is being converted to energy", says Sano. The work is published by Nature Physics today1.
The team's set-up was inspired by a nineteenth-century thought experiment proposed by Scottish physicist James Clerk Maxwell, which — controversially, at the time — suggested that information could be converted into energy. In the thought experiment, a demon guards a door between two rooms, each filled with gas molecules. The demon allows only fast-moving gas particles to pass out of the room on the left and into the room on the right, and only slow-moving particles to pass in the opposite direction.
As a result, the room on the right gradually gets warmer as the average speed of particles in that room increases, and the room on the left gets colder. The demon thus creates a difference in temperature without ever imparting any energy directly to the gas molecules — simply by knowing information about their speeds. This seems to violate the second law of thermodynamics, which states that you cannot make a system more ordered without any energy input.
The experiment does not actually violate the second law of thermodynamics, because in the system as a whole, energy must be consumed by the equipment — and the experimenters — to monitor the bead and switch the voltage as needed. But it does show that information can be used as a medium to transfer energy, says Sano. The bead is driven as a mini-rotor, with a information-to-energy conversion efficiency of 28%.
Is it possible that both interpretations - the unified state where everything happens "at once" - as well as the informational, linear state, describe the two sides of what is occurring?