About the Higgs boson in ars technica article 'Narrowing in on the Higgs boson'
"Since the LHC is anticipated to produce its first collisions later this year, it may not be long before we obtain clear evidence of the existence of the Higgs boson. I tend to think that this would be one of the least exciting answers possible, though. The real scientific treat would be if the LHC and other colliders can't find any Higgs particles. This would mean that the standard model, one of the shining examples of the power of particle physics and a theory on which a lot of physics rests, might be wrong; we would have to go back to the drawing board and invent something new."
Attributed as 'real scientific treat' if the colliders do not find any proof of the Higgs boson existence? Why would my mind stop at that particular sentence?
It is not its existence that is doubted, ... but its existence in a ... free form in the universe? ... that the universe is inhabited by a vast number of Higgs bosons, hiding obscuring their presence? ... it is what part of the universe they inhabit, it's what matters.
While this is unlikely, seeing as how the experimentalists have found 60 of the 61 particles that appear within the standard model, it sure would make the next few years interesting, both for scientists in the field and interested third parties like science journalists."
Sunday, 29 March 2009
Monday, 23 March 2009
Archimedes actual infinities, as revealed in his lost manuscript.
Archimedes actual infinities, as revealed in his lost manuscript.
I read in the article 'A Prayer for Archimedes', about the long-lost text by the ancient Greek mathematician which shows that he had begun to discover the principles of calculus.
In the claim put forward by Reviel Netz, an historian of mathematics at Stanford University who transcribed the newly found text, says that the recent discoveries show that Archimedes indeed used the notion of actual infinity.
Infinities, as defined by Aristotle, mentioned here
"The Greek philosopher Aristotle built defenses against infinity's vexing qualities by distinguishing between the "potential infinite" and the "actual infinite." An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn't exist."
An infinitely long line would be actually infinite, hence actual infinity, whereas a line that could always be extended would be potentially infinite, hence potential infinity. Aristotle argued that the actual infinity didn't exist.
I read further
"Archimedes found a relationship between the full area of that slice, which was a section through the plane-sided volume, and the smaller area within it, which was a section through the curved shape. Then he argued that he could use that relationship to calculate the entire volume of the curved shape, because both the curved figure and the straight one contained the same number of slices."
and
"That number just happened to be infinity—actual infinity."
and
"The interesting breakthrough is that he is completely willing to operate with actual infinity," Netz says, but he adds that "the argument is definitely not completely valid. He just had a strong intuition that it should work." In this case, it did work, but it remained for Newton and Leibniz to figure out how to make the argument mathematically rigorous."
Archimedes being willing to operate with actual infinity, an infinitely long line, instead of a line that could always be extended. A potentially infinite line, what Aristotle argued that exists, whereas the actual infinity did not exist.
So, there is not infinity as such, whatever name it can be given, actual or potential, since an infinite line can always be extended. There are no boundaries.
But the infinity of decimal numbers, lying between two integer numbers, it has boundaries. The two integer numbers that lies within. Does having boundaries determine the kind of infinity it is? The infinity of decimal numbers between two integers, can not be extended beyond the integer boundaries.
It cannot be potentially infinite, it can only be actual infinity, what the calculus uses. What has driven Archimedes "strong intuition that it should work", and why "In this case, it did work". And it works when dealing with infinities that the boundaries are known or postulated beforehand.
What "it remained for Newton and Leibniz to figure out, how to make the argument mathematically rigorous.
Confusing the issues amidst vague statements, if "the argument is definitely not completely valid." What is valid, what is completely valid, what is not completely valid, and what is definitely not completely valid. How is validity defined, what is required to make an argument valid.
I read further in the same article
"Newton and Leibniz also worked with actual infinity. Leibniz went so far as to say in a letter, "I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author."
Since Newton and Leibniz also worked with actual infinity and produced calculus, would that not validate Archimedes intuition and his willingness to operate with actual infinity?
And what is meant by Leibniz' statement that nature makes frequent use of it, everywhere. Does that not imply the fractality inherent in all nature's objects, chaos driven processes surpassing, traversing fractal dimensions, from the microscales to the macroscales weaving the perfections of its author, chaos. Actual infinities trapped within the delimiting boundaries of any nature's object, all objects.
The statement 'modern calculus no longer makes use of the actual infinite; it sticks with Aristotle's distinction', a matter of taste?
I read in the article 'A Prayer for Archimedes', about the long-lost text by the ancient Greek mathematician which shows that he had begun to discover the principles of calculus.
In the claim put forward by Reviel Netz, an historian of mathematics at Stanford University who transcribed the newly found text, says that the recent discoveries show that Archimedes indeed used the notion of actual infinity.
Infinities, as defined by Aristotle, mentioned here
"The Greek philosopher Aristotle built defenses against infinity's vexing qualities by distinguishing between the "potential infinite" and the "actual infinite." An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn't exist."
An infinitely long line would be actually infinite, hence actual infinity, whereas a line that could always be extended would be potentially infinite, hence potential infinity. Aristotle argued that the actual infinity didn't exist.
I read further
"Archimedes found a relationship between the full area of that slice, which was a section through the plane-sided volume, and the smaller area within it, which was a section through the curved shape. Then he argued that he could use that relationship to calculate the entire volume of the curved shape, because both the curved figure and the straight one contained the same number of slices."
and
"That number just happened to be infinity—actual infinity."
and
"The interesting breakthrough is that he is completely willing to operate with actual infinity," Netz says, but he adds that "the argument is definitely not completely valid. He just had a strong intuition that it should work." In this case, it did work, but it remained for Newton and Leibniz to figure out how to make the argument mathematically rigorous."
Archimedes being willing to operate with actual infinity, an infinitely long line, instead of a line that could always be extended. A potentially infinite line, what Aristotle argued that exists, whereas the actual infinity did not exist.
So, there is not infinity as such, whatever name it can be given, actual or potential, since an infinite line can always be extended. There are no boundaries.
But the infinity of decimal numbers, lying between two integer numbers, it has boundaries. The two integer numbers that lies within. Does having boundaries determine the kind of infinity it is? The infinity of decimal numbers between two integers, can not be extended beyond the integer boundaries.
It cannot be potentially infinite, it can only be actual infinity, what the calculus uses. What has driven Archimedes "strong intuition that it should work", and why "In this case, it did work". And it works when dealing with infinities that the boundaries are known or postulated beforehand.
What "it remained for Newton and Leibniz to figure out, how to make the argument mathematically rigorous.
Confusing the issues amidst vague statements, if "the argument is definitely not completely valid." What is valid, what is completely valid, what is not completely valid, and what is definitely not completely valid. How is validity defined, what is required to make an argument valid.
I read further in the same article
"Newton and Leibniz also worked with actual infinity. Leibniz went so far as to say in a letter, "I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author."
Since Newton and Leibniz also worked with actual infinity and produced calculus, would that not validate Archimedes intuition and his willingness to operate with actual infinity?
And what is meant by Leibniz' statement that nature makes frequent use of it, everywhere. Does that not imply the fractality inherent in all nature's objects, chaos driven processes surpassing, traversing fractal dimensions, from the microscales to the macroscales weaving the perfections of its author, chaos. Actual infinities trapped within the delimiting boundaries of any nature's object, all objects.
The statement 'modern calculus no longer makes use of the actual infinite; it sticks with Aristotle's distinction', a matter of taste?
Thursday, 5 March 2009
Suffocating within the narrow, self-imposed boundaries of ideologies
Ideologies, dogmas, doctrines developed, their whole range starting from anarchy and communism on one end to its other end of the spectrum capitalism and fascism, individuals deeply entrenched, they are all, being so absolute, try hard to convince you, that their way of thinking, is the only way of thinking.
Calling it the truth, their very own version of truth.
The concept of truth is non-existent. Its alleged attributes can not be realised outside the mind of the single individual and as such it assumes a variety of contents. This essayist gives its own account on that matter, a clearer perspective avoiding muddling the issue further.
Adhering to the truth or truths individuals resist, deny themselves the exposure to myriads of new concepts and drives them into ignorance and by that stupidity, as less and less stimuli, (how information around us arouse, excites and triggers thoughts in our minds), are taken into consideration, or even information pass unseen, unnoticed, unregistered by our senses and our mind's attention.
Loosing themselves in the complexity, perplexing, ever-expanding, constantly creating and re-creating itself, without realizing that all that enormous complexity suffocates within narrow and limiting boundaries. Bloated to the hilt, squeezing and stretching its rigid boundaries to no avail and certainly unable to offer any viable solutions to problems faced, loosing touch with reality.
A complexity, as such, with an infinite capacity, the same infinite capacity in fitting decimal numbers between the numbers 1 and 2. You have an infinite cohort of numbers from 1,01..... to 2.99998 that lie there but can never pass below number 1 or above number 2.
In the same way all their intellect's productive output, the ideas they carry and develop, it will never pass the narrow boundaries set by their prospective ideologies, dogmas or doctrines or whatever other way it can be called, or the so much revered truth construct. The truths they adhere to.
An educated ignorance, which denies the use of the most valuable of our brain's and mind's processes, that worths a lot. That of the ability to make the strange familiar and the familiar strange.
Calling it the truth, their very own version of truth.
The concept of truth is non-existent. Its alleged attributes can not be realised outside the mind of the single individual and as such it assumes a variety of contents. This essayist gives its own account on that matter, a clearer perspective avoiding muddling the issue further.
Adhering to the truth or truths individuals resist, deny themselves the exposure to myriads of new concepts and drives them into ignorance and by that stupidity, as less and less stimuli, (how information around us arouse, excites and triggers thoughts in our minds), are taken into consideration, or even information pass unseen, unnoticed, unregistered by our senses and our mind's attention.
Loosing themselves in the complexity, perplexing, ever-expanding, constantly creating and re-creating itself, without realizing that all that enormous complexity suffocates within narrow and limiting boundaries. Bloated to the hilt, squeezing and stretching its rigid boundaries to no avail and certainly unable to offer any viable solutions to problems faced, loosing touch with reality.
A complexity, as such, with an infinite capacity, the same infinite capacity in fitting decimal numbers between the numbers 1 and 2. You have an infinite cohort of numbers from 1,01..... to 2.99998 that lie there but can never pass below number 1 or above number 2.
In the same way all their intellect's productive output, the ideas they carry and develop, it will never pass the narrow boundaries set by their prospective ideologies, dogmas or doctrines or whatever other way it can be called, or the so much revered truth construct. The truths they adhere to.
An educated ignorance, which denies the use of the most valuable of our brain's and mind's processes, that worths a lot. That of the ability to make the strange familiar and the familiar strange.
Tuesday, 3 March 2009
Consciousness whole pattern processing regime.
Patterns. You bring along the whole pattern for consciousness to process. In units as it is mentioned in, 'Is consciousness only a property of individual cells?', by Jonathan CW Edwards,
"The second, which I will call the physical substrate, is that of finding a substrate at the fundamental physical level which might support a subjective experience in which many elements are bound into a seamless whole."
Many elements bound into a seamless whole! Each element is, in its turn and for its own accord, a seamless whole made out of or bound from its own specific elements, downscale as far as it is permitted by the granularity (?) of the physical world. Granules, as a general term referring to the size of the physical units possible? Up to quanta or strings?
As a seamless whole is presented to our consciousness as whole patterns and processed as such. All the information elements bound in the pattern, are dragged along, no matter how relevant they appear to be. Even if they are seemingly incompatible or contradict with one another.
Emergence? And its incompatibility pre-requisite for emergent properties to rise? The consciousness whole pattern processing allowing emergence to appear? Working towards achieving that goal?
"The second, which I will call the physical substrate, is that of finding a substrate at the fundamental physical level which might support a subjective experience in which many elements are bound into a seamless whole."
Many elements bound into a seamless whole! Each element is, in its turn and for its own accord, a seamless whole made out of or bound from its own specific elements, downscale as far as it is permitted by the granularity (?) of the physical world. Granules, as a general term referring to the size of the physical units possible? Up to quanta or strings?
As a seamless whole is presented to our consciousness as whole patterns and processed as such. All the information elements bound in the pattern, are dragged along, no matter how relevant they appear to be. Even if they are seemingly incompatible or contradict with one another.
Emergence? And its incompatibility pre-requisite for emergent properties to rise? The consciousness whole pattern processing allowing emergence to appear? Working towards achieving that goal?
Thursday, 5 February 2009
Darwinism. A hideous aspect?
Hot-footing towards justifying the inequalities writhing in societies the world over? Aimed at making sure that individuals yield to the power of states, states overrun by a handful of individuals whose only and single goal is to accumulate riches, forcing every one else to submission? ... to their will?
Providing the ideological framework for a fertile ground where mottoes of everybody against everyone else, kill or be killed, my survival runs through your extinction, proliferate. The jungle rules ok amidst our societies. A poor metaphor, remnant of the british colonial era ideas still held tight in the minds of people, ridiculous when someone brings into mind the present state of jungles, decimated by the western philosophies spread-out notions of, ecological cleansing and ruthless exploitation.
Is it just an attempt, for people to find acceptable the current state of affairs, the world over? The domination by the fittest of the weak of our world?
That there some of us that are better than the rest of humanity? And these better individuals deserve more than every other individual put together? That they even deserve first ticket in the rat-ship out of this world, as it heads towards its certain doom, when is proved to be beyond redemption, destined to oblivion? And the rest of humanity, the undeserved, will be left behind, to be extinguished along the ravaged by the unscrupulous exploitation in the pursuit for ever more profits, planet? To suffer the consequences and be sacrificed?
What is hidden behind the triumph of natural selection, that they so admire? The ruthless struggle for survival, the proverbial jungle the world is. The human affairs ruthlessly distorted, pervaded in every aspect human relationships are nowadays, out in a never-ending competition. Is that what it is? Competition that could lead to extinction of the weak?
What kind of thoughts, the remark of Richard Fortey, quoted here, can lead to?
"How does evolution produce enormously species-rich genera, such as Eucalyputus, many of which can co-exist happily in the same habitat?"
... co-exist happily in the same habitat? Something along the lines of
"The model posits a complete replacement of one generation by another better-adapted generation? Generations in each bifurcation point, of a linearly developed evolutionary tree, present all the 'initial conditions' for the next stage of evolution to take place? 'Initial conditions' in the context of chaos? The sensitive dependence and all that, that will determine the next better-adapted generation?"
coming through out of the findings mentioned here
"Rather than a competition occurring, the model posits a complete replacement of one generation by another better-adapted generation."
Providing the ideological framework for a fertile ground where mottoes of everybody against everyone else, kill or be killed, my survival runs through your extinction, proliferate. The jungle rules ok amidst our societies. A poor metaphor, remnant of the british colonial era ideas still held tight in the minds of people, ridiculous when someone brings into mind the present state of jungles, decimated by the western philosophies spread-out notions of, ecological cleansing and ruthless exploitation.
Is it just an attempt, for people to find acceptable the current state of affairs, the world over? The domination by the fittest of the weak of our world?
That there some of us that are better than the rest of humanity? And these better individuals deserve more than every other individual put together? That they even deserve first ticket in the rat-ship out of this world, as it heads towards its certain doom, when is proved to be beyond redemption, destined to oblivion? And the rest of humanity, the undeserved, will be left behind, to be extinguished along the ravaged by the unscrupulous exploitation in the pursuit for ever more profits, planet? To suffer the consequences and be sacrificed?
What is hidden behind the triumph of natural selection, that they so admire? The ruthless struggle for survival, the proverbial jungle the world is. The human affairs ruthlessly distorted, pervaded in every aspect human relationships are nowadays, out in a never-ending competition. Is that what it is? Competition that could lead to extinction of the weak?
What kind of thoughts, the remark of Richard Fortey, quoted here, can lead to?
"How does evolution produce enormously species-rich genera, such as Eucalyputus, many of which can co-exist happily in the same habitat?"
... co-exist happily in the same habitat? Something along the lines of
"The model posits a complete replacement of one generation by another better-adapted generation? Generations in each bifurcation point, of a linearly developed evolutionary tree, present all the 'initial conditions' for the next stage of evolution to take place? 'Initial conditions' in the context of chaos? The sensitive dependence and all that, that will determine the next better-adapted generation?"
coming through out of the findings mentioned here
"Rather than a competition occurring, the model posits a complete replacement of one generation by another better-adapted generation."
Labels:
competition,
Darwinism,
ideological framework,
inequalities
Tuesday, 3 February 2009
Abolish money. How?
Abolishing money can not be taken as an act of revenge on any 'in-whatever-way-it-can-be-assumed" wrong-doers of an age past. Emerging societies where money are abolished can not be thought off according to the standards prevailing in societies nowadays. It is a goal to be reached and the only thing it can be done in our present age and time is to sow the seeds for its coming. As the human individual, in either collective or individual level is unable or incapable to forsee the ensued complexity in human relationships that lies ahead.
It is not or it will not be the triumph of socialism or any other kind of system upon other. It is not going to be the result of class struggle but instead of co-operation among individuals regardless their background. I would say it precludes and excludes any system of government currently present the world over, in fact any such system would be abolished before money are abolished. It is not a system where individual or collective will can be forced upon any single or group of individuals. Wealth would be a valid concept, no more.
Government will shed its cloak of power and the administrators duty will be just as any other duty, any other individual undertakes. It is a path that all human individuals will tread alongside each other, humanity in its natural course where all individuals are accounted for.
It is not or it will not be the triumph of socialism or any other kind of system upon other. It is not going to be the result of class struggle but instead of co-operation among individuals regardless their background. I would say it precludes and excludes any system of government currently present the world over, in fact any such system would be abolished before money are abolished. It is not a system where individual or collective will can be forced upon any single or group of individuals. Wealth would be a valid concept, no more.
Government will shed its cloak of power and the administrators duty will be just as any other duty, any other individual undertakes. It is a path that all human individuals will tread alongside each other, humanity in its natural course where all individuals are accounted for.
Labels:
abolish money,
co-operation,
government,
humanity,
wealth
Friday, 23 January 2009
Complete replacement rather than competition? And initial conditions looked at, from a chaos perspective.
Threads connected with these thoughts
- Evolutionary process more detailed than previously believed, study shows
- Throwing overboard relentlessly whatever is remotely connected with what is not agreed now.
I read in Darwin was wrong...ish
"Instead, that model adopts a linear approach, theorizing that a population acquires such adaptations successively, one after another. Rather than a competition occurring, the model posits a complete replacement of one generation by another better-adapted generation."
A linear approach? Adaptations acquired successively, one after another? Bifurcations? The model posits a complete replacement of one generation by another better-adapted generation? Generations in each bifurcation point, of a linearly developed evolutionary tree, present all the 'initial conditions' for the next stage of evolution to take place? 'Initial conditions' in the context of chaos? The sensitive dependence and all that, that will determine the next better-adapted generation? The complete replacement of the generation past, reminiscent of what takes place when a paradigm shift happens? Along the lines of 'anything adhered to before a paradigm shift is completely forgotten, abandoned, thrown overboard'.
Competition is a hogwash?
It's worth more than a furtive look.
The same goes for what is mentioned in this article as well
'Evolutionary process more detailed than previously believed, study shows'
- Evolutionary process more detailed than previously believed, study shows
- Throwing overboard relentlessly whatever is remotely connected with what is not agreed now.
I read in Darwin was wrong...ish
"Instead, that model adopts a linear approach, theorizing that a population acquires such adaptations successively, one after another. Rather than a competition occurring, the model posits a complete replacement of one generation by another better-adapted generation."
A linear approach? Adaptations acquired successively, one after another? Bifurcations? The model posits a complete replacement of one generation by another better-adapted generation? Generations in each bifurcation point, of a linearly developed evolutionary tree, present all the 'initial conditions' for the next stage of evolution to take place? 'Initial conditions' in the context of chaos? The sensitive dependence and all that, that will determine the next better-adapted generation? The complete replacement of the generation past, reminiscent of what takes place when a paradigm shift happens? Along the lines of 'anything adhered to before a paradigm shift is completely forgotten, abandoned, thrown overboard'.
Competition is a hogwash?
It's worth more than a furtive look.
The same goes for what is mentioned in this article as well
'Evolutionary process more detailed than previously believed, study shows'
Labels:
competition,
Darwin,
initial conditions,
paradigm shift
Wednesday, 14 January 2009
Sub-atomic particles having zero rest mass. Universe, an infinitesimally thin sheet?
.... mass itself an emergent product?
I read in New Scientist of 3 February 2001, article 'Mass medium' pp. 22-25, in page 25 excerpt titled 'Mass delusion'
"Most theories that attempt to unify the forces of nature, showing them to be facets of a single "superforce", treat all subatomic particles as having zero rest mass. So they need an extra ingredient-the Higgs boson."
Sub-atomic particles having zero rest mass? Sub-atomic particles? What our universe is made up of? Having zero mass? Mass which fills the universe? What makes it appear to us, as an enormous void full of massive objects? Compact, solid? But the stuff of these massive objects, the sub-atomic particles, have zero rest mass?
So, the whole universe can easily fit in a sheet of infinitesimal thickness?
As what I thought in "Observer to Planck length distance, fractal? Why we perceive continuity, out of the energy packets (quanta), the physical world is made out of?", post
"For any effect, the world we live in, the reality for us, might unravel in infinite fractal dimensions inside thin sheets, as thick as A4 paper."
I read in New Scientist of 3 February 2001, article 'Mass medium' pp. 22-25, in page 25 excerpt titled 'Mass delusion'
"Most theories that attempt to unify the forces of nature, showing them to be facets of a single "superforce", treat all subatomic particles as having zero rest mass. So they need an extra ingredient-the Higgs boson."
Sub-atomic particles having zero rest mass? Sub-atomic particles? What our universe is made up of? Having zero mass? Mass which fills the universe? What makes it appear to us, as an enormous void full of massive objects? Compact, solid? But the stuff of these massive objects, the sub-atomic particles, have zero rest mass?
So, the whole universe can easily fit in a sheet of infinitesimal thickness?
As what I thought in "Observer to Planck length distance, fractal? Why we perceive continuity, out of the energy packets (quanta), the physical world is made out of?", post
"For any effect, the world we live in, the reality for us, might unravel in infinite fractal dimensions inside thin sheets, as thick as A4 paper."
Labels:
rest mass,
sheet,
sub-atomic particles,
universe
Sunday, 11 January 2009
Chaos traces in Ed Fredkin's digital philosophy?
Exciting aspects, in what I have read in Cellular automaton models in Digital Philosophy website which compels me to write them down, raw as they are.
The following extract from Chapter 1 Cellular automaton models
"Our thesis is that some CA model may be, in effect, programmed to act like physics. We call such models digital mechanics (DM). In short, DM is a discrete and deterministic modelling system which we propose to use (instead of differential equations, for example) for modelling phenomena in physics. We are driven in this direction by many heuristics; primarily by the concept, borrowed (and extended) from automata theory, of the universal machine [3] Any ordinary commercial computer would be a universal machine, except for the fact that it does not have an infinite memory. In this paper, we shall extend the meaning of the term "universal machine" to include the universal cellular automaton (UCA) or other kinds of general purpose computers that have large but finite memories; this would include any commercial computer. A universal machine can exactly mimic the behavior of any other finite computer, provided its memory is just a very little bit larger than the target machine."
referring to the universal cellular automaton model, as being based on the concept of the universal machine, which can exactly mimic 'behaviours' applicable to wider and varied settings?
Is it directly related with the universality principle prevalent in chaos, or is it a simple circumstantial connection? Intended or unintended? It is worth pursuing that line of thinking.
And further
"By "complexity" we mean some combination of: a large number of states per cell, a complex CA rule, neighborhood (spatial connectivity and dimensionality), boundary condition or initial condition."
the mention of 'boundary condition or initial condition', brings into mind chaos's 'sensitive dependence on initial conditions', and that notion combined with the statement
" RUCA also exhibit unusual and counterintuitive behavior that is a consequence of perfect reversibility combined with extreme quantization."
where the 'unusual and counterintuitive behavior', being the hallmark of chaos developing states, as well as from the phrase 'a consequence of perfect reversibility combined with extreme quantization', the mention of 'extreme quantization', strengthening the ties of the RUCA model with chaos via its sensitive dependence on the minutiae of changes in initial conditions.
Which is further exacerbated in the paragraph
"RUCA reversibility is very different than the intuitive notion of microscopic reversibility that relies on continuity to ensure that no effect gets lost no matter how infinitesimal it becomes."
initial conditions preserved no matter how 'infinitesimal' they become.
Remarks that sink deeper into my mind the chaotic origins of reality.
The following extract from Chapter 1 Cellular automaton models
"Our thesis is that some CA model may be, in effect, programmed to act like physics. We call such models digital mechanics (DM). In short, DM is a discrete and deterministic modelling system which we propose to use (instead of differential equations, for example) for modelling phenomena in physics. We are driven in this direction by many heuristics; primarily by the concept, borrowed (and extended) from automata theory, of the universal machine [3] Any ordinary commercial computer would be a universal machine, except for the fact that it does not have an infinite memory. In this paper, we shall extend the meaning of the term "universal machine" to include the universal cellular automaton (UCA) or other kinds of general purpose computers that have large but finite memories; this would include any commercial computer. A universal machine can exactly mimic the behavior of any other finite computer, provided its memory is just a very little bit larger than the target machine."
referring to the universal cellular automaton model, as being based on the concept of the universal machine, which can exactly mimic 'behaviours' applicable to wider and varied settings?
Is it directly related with the universality principle prevalent in chaos, or is it a simple circumstantial connection? Intended or unintended? It is worth pursuing that line of thinking.
And further
"By "complexity" we mean some combination of: a large number of states per cell, a complex CA rule, neighborhood (spatial connectivity and dimensionality), boundary condition or initial condition."
the mention of 'boundary condition or initial condition', brings into mind chaos's 'sensitive dependence on initial conditions', and that notion combined with the statement
" RUCA also exhibit unusual and counterintuitive behavior that is a consequence of perfect reversibility combined with extreme quantization."
where the 'unusual and counterintuitive behavior', being the hallmark of chaos developing states, as well as from the phrase 'a consequence of perfect reversibility combined with extreme quantization', the mention of 'extreme quantization', strengthening the ties of the RUCA model with chaos via its sensitive dependence on the minutiae of changes in initial conditions.
Which is further exacerbated in the paragraph
"RUCA reversibility is very different than the intuitive notion of microscopic reversibility that relies on continuity to ensure that no effect gets lost no matter how infinitesimal it becomes."
initial conditions preserved no matter how 'infinitesimal' they become.
Remarks that sink deeper into my mind the chaotic origins of reality.
Fractal corridors? Existence, reality, universe is built by?
Fractal corridors?
... harboring even cosmic strings?
... by which Mach's principle acquire substance? The ties of each atom, each quantum particle with every other atom in the universe?
... constraining energy, ever since the big bang, separating it into the different kinds of fundamental forces existing now in the universe?
... giving substance to Ed Fredkin's idea of a universe built out of automata? Ed Fredkin's cells being fractal pockets?
... harboring even cosmic strings?
... by which Mach's principle acquire substance? The ties of each atom, each quantum particle with every other atom in the universe?
... constraining energy, ever since the big bang, separating it into the different kinds of fundamental forces existing now in the universe?
... giving substance to Ed Fredkin's idea of a universe built out of automata? Ed Fredkin's cells being fractal pockets?
Wednesday, 7 January 2009
Fractal universe, fractal reality?
I read in New Scientist of 3 February 2001, article 'Mass medium' pp. 22-25, in page 24
"Rather than being empty, the vacuum is a choppy sea of randomly fluctuating electromagnetic waves. We don't see or feel them because they pop in and out of existence incredibly quickly, appearing only for a split second. These fleeting apparitions are called virtual photons."
'In and out of existence'? What is that existence? How can we fathom it? Describe it, define it. Is it reality proper, and specifically its lowest level? As space being there, created to accommodate, to contain infinitesimal particles, their energy halo, their fields? A space, a reference frame, within a more fundamental space as it comes out from what Ed Fredkin says, in New Scientist of 21 June 2003, article 'In the beginning was the Rule' pp. 32-35, in page 35,
"Fredkin says such objections arise because other people do not understand the concept of space he is working with. 'The space of physics isn't defined by the cellular array', he says. 'It's defined by the paths that free particles take in the cellular array'."
The space Ed Fredkin came up with, working on his theory based on cellular automata, is more fundamental, underlying the space physics study, including the 'existence' of virtual particles, that pop in and out it. 'It' being existence. What if, following the leads given above, assume that the virtual particles primarily exist in the fundamental space, Ed Fredkin proclaims. By virtue of their designated name, 'virtual' particles, therefore attribute the underlying fundamental space as 'virtual' space, where they reside and from there, they make their fleeting appearances in the 'existence', physics observes and measures.
Invade our familiar space, and reveal their existence more likely, than pop in and out of existence. What if, the cells in Ed Fredkin's digital universe, are fractal cells, virtually fractal corridors, extremely thin, or thin enough to accommodate photons, permeating the universe, indicating its nature, a fractal universe, a fractal reality.
The virtual particles teeming the vacuum, simply being the cross-sections of universe's fractal corridors passed by, in the endless motion of particles within.
"Rather than being empty, the vacuum is a choppy sea of randomly fluctuating electromagnetic waves. We don't see or feel them because they pop in and out of existence incredibly quickly, appearing only for a split second. These fleeting apparitions are called virtual photons."
'In and out of existence'? What is that existence? How can we fathom it? Describe it, define it. Is it reality proper, and specifically its lowest level? As space being there, created to accommodate, to contain infinitesimal particles, their energy halo, their fields? A space, a reference frame, within a more fundamental space as it comes out from what Ed Fredkin says, in New Scientist of 21 June 2003, article 'In the beginning was the Rule' pp. 32-35, in page 35,
"Fredkin says such objections arise because other people do not understand the concept of space he is working with. 'The space of physics isn't defined by the cellular array', he says. 'It's defined by the paths that free particles take in the cellular array'."
The space Ed Fredkin came up with, working on his theory based on cellular automata, is more fundamental, underlying the space physics study, including the 'existence' of virtual particles, that pop in and out it. 'It' being existence. What if, following the leads given above, assume that the virtual particles primarily exist in the fundamental space, Ed Fredkin proclaims. By virtue of their designated name, 'virtual' particles, therefore attribute the underlying fundamental space as 'virtual' space, where they reside and from there, they make their fleeting appearances in the 'existence', physics observes and measures.
Invade our familiar space, and reveal their existence more likely, than pop in and out of existence. What if, the cells in Ed Fredkin's digital universe, are fractal cells, virtually fractal corridors, extremely thin, or thin enough to accommodate photons, permeating the universe, indicating its nature, a fractal universe, a fractal reality.
The virtual particles teeming the vacuum, simply being the cross-sections of universe's fractal corridors passed by, in the endless motion of particles within.
Saturday, 3 January 2009
Convention? What kind of convention is that? Agreement or compromise?
"By convention there is color, by convention there is sweetness, by convention bitterness, but in realty there are atoms and space.
—Democritus"
Convention? What kind of convention is that? Agreement or compromise?
Convention? Like interpretation? How the mind instantiates 'realty'? Or, how human minds, as a 'populace' agreed to look upon 'realty'? A second stage act following a first stage act of a single human mind observing 'realty', and after that, it passes its concluded thoughts about the observations, as it sits down with other mind-bearers to agree to a common approach. On how to interpret the conclusions amassed, provide a name-symbol, and use it to depict what is conceived? The stuff of concepts? Reaching an accord? At least that is how reason should work.
Or is it convention within a single mind, that makes the 'atoms and space' realty into something that agrees with its unit make-up, its senses and its body? And since, its senses and its body, are what it has to work with, it can not do anything else, but use them. Convention being more like a compromise? Its unit make-up, a result of endless processes between the 'atoms and space', that realty is, have confined the individual in a level of existence, isolated from all other levels above and below, trapped, bound by impenetrable boundaries? Only its mind is left out free to roam at any level, up or down, and beyond? Traverse right down to the bottom levels, even further below than 'atoms and space' lay?
The space of the DM is certainly not the space of the RUCA.
Why is the mind capable to traverse impenetrable boundaries? Is it because what lies down there, is made out of the stuff, the mind is made up from?
—Democritus"
Convention? What kind of convention is that? Agreement or compromise?
Convention? Like interpretation? How the mind instantiates 'realty'? Or, how human minds, as a 'populace' agreed to look upon 'realty'? A second stage act following a first stage act of a single human mind observing 'realty', and after that, it passes its concluded thoughts about the observations, as it sits down with other mind-bearers to agree to a common approach. On how to interpret the conclusions amassed, provide a name-symbol, and use it to depict what is conceived? The stuff of concepts? Reaching an accord? At least that is how reason should work.
Or is it convention within a single mind, that makes the 'atoms and space' realty into something that agrees with its unit make-up, its senses and its body? And since, its senses and its body, are what it has to work with, it can not do anything else, but use them. Convention being more like a compromise? Its unit make-up, a result of endless processes between the 'atoms and space', that realty is, have confined the individual in a level of existence, isolated from all other levels above and below, trapped, bound by impenetrable boundaries? Only its mind is left out free to roam at any level, up or down, and beyond? Traverse right down to the bottom levels, even further below than 'atoms and space' lay?
The space of the DM is certainly not the space of the RUCA.
Why is the mind capable to traverse impenetrable boundaries? Is it because what lies down there, is made out of the stuff, the mind is made up from?
Labels:
atoms and space,
convention,
Democritus,
digital philosophy,
Ed Fredkin,
reality
Saturday, 27 December 2008
As space expands outwards since the big bang, it expands inwards too?
Relevant posts
- Fractal dimensions harbour parallel worlds?
- Observer to Planck length distance, fractal? Why we perceive continuity, out of the energy packets (quanta), the physical world is made out of?
I read in Answers.com, 'cosmic background radiation' entry
"This big bang was not an explosion of matter into empty space but an explosion of space itself."
Space was not there, and space was created? The notions of microscopic and macroscopic were irrelevant at that time?
Space flat? No depth?
As space exploded, it expanded both ways? Deeper in to the microscopic, creating the quantum world and further out in the macroscopic world, creating the universe?
Mirror images? And as such, the quantum world expands deeper and deeper in as the universe expands further and further away?
With the speed of light? Which might have implications on the electron to nucleus distance?
The microcosm expanding? But this runs counter to common held notions of the microscopic world. Countless pockets of microcosms, apparent. Fractal? Fractal origins for every atom in our bodies, in the world at large?
Energy dissipated down fractal paths, as space expanded deeper and deeper in, forces eventually being constrained in fractal corridors, effectively separated into the kinds that exist now?
- Fractal dimensions harbour parallel worlds?
- Observer to Planck length distance, fractal? Why we perceive continuity, out of the energy packets (quanta), the physical world is made out of?
I read in Answers.com, 'cosmic background radiation' entry
"This big bang was not an explosion of matter into empty space but an explosion of space itself."
Space was not there, and space was created? The notions of microscopic and macroscopic were irrelevant at that time?
Space flat? No depth?
As space exploded, it expanded both ways? Deeper in to the microscopic, creating the quantum world and further out in the macroscopic world, creating the universe?
Mirror images? And as such, the quantum world expands deeper and deeper in as the universe expands further and further away?
With the speed of light? Which might have implications on the electron to nucleus distance?
The microcosm expanding? But this runs counter to common held notions of the microscopic world. Countless pockets of microcosms, apparent. Fractal? Fractal origins for every atom in our bodies, in the world at large?
Energy dissipated down fractal paths, as space expanded deeper and deeper in, forces eventually being constrained in fractal corridors, effectively separated into the kinds that exist now?
Labels:
big bang,
distance fractal?,
fractal
Thursday, 4 December 2008
Observer to Planck length distance, fractal? Why we perceive continuity, out of the energy packets (quanta), the physical world is made out of?
Space an emergent product?
Italicized journey of thoughts, emanated by naive observations badly, anything but eloquently, expressed but nevertheless building towards new perspectives in my mind, as I gradually assimilate, (my very own meaning construction process), informed, worked-out assumptions presented by experts in the field
Heck! I forgot about that. The four blinking lights in two rows and two columns, (a matrix(?)), a rectangle near square, surrounding a two-digit number display(?). Alternate blinking of the lights per row. The two lights lying on a row were lit at the same time. One time interval, 1 time-step, then off. In the next time-step, the lights in the other row were lit, then off. Alternate lighting up per row continuously. The lights, as looked from afar gave the impression of a light running up and down. The perception of a single(!)... (the whole(?)) light jumping up and down incessantly. The lights, as being looked at, from near, did not give the impression of a running light, instead each single light in the row was constantly switched on and off. The illusion or perception of a running light, a shining beam going up and down, only given by the lights looked at from afar, but not when looked at from near. Distance of the lights from the observer being crucial? For the illusion of a running light(!) to be perceived by the observer.
Light, transmitted as waves. In both cases by different sources, but the distance from the observer would make a difference in its perception. What it is perceived. In my mind, this is how waves are perceived in our minds, and by that reality. Distance being crucial in the way waves are perceived. It is connected with perceived coherence and our ability to distinguish between simultaneously emitted waves. It is what I dealt with, as well, after I read this article about the human resolving time.
Anyhow, it evades me at the moment, but the thought that occurred to me, is connected with the microscopic world, the world of quanta.
Oumf, space being an emergent phenomenon? There is no actually space, we do not really probe space, as it is not there? It emerges as a result of the processes involved. That even flat, let's call it space, is sufficient to describe it as. The branes, to use a word from string theory, a flat surface that contains or includes, all our universe. The onion with its laid-out skins of fractal universes?
And to go back to the idea of distance being crucial to how we perceive incoming waves. Waves from atomic and sub-atomic particles, quanta for that matter, as they are perceived by virtue of the energy, they emit; in waves, each by itself a unique, single source, but what we experience, by virtue of a function(?) that combines all these waves to the reality perceived? As it emerges as reality?
And where the waves come from? They come from a distance quite afar and that's why we perceive them as running or interacting with one another.
A distance that increases as we go deeper and deeper into the microscopic world? which even creates the impression of interaction?
Interference of the waves, which we mistake as motion?
Distance, as it is experienced in the classical world and distance, by which, out of the quanta, the packets emitted, we perceive the world as is?
(in a manner analogous to combined?)
That all reality can be explained by looking at it from that angle, distance; distance from the observer, the human individual. To begin with there is the quanta, packets of energy, waves. As the waves are dispatched in packets, effectively blink, incessantly, and the observer which senses these processes from a distance; far far away; namely the distance to the microscales, to Planck length itself. A distance so remote and yet so close? The observer surmises continuity out of the stream of packets, and by that reality?
How can that happen?
Distance should not be conceived as a straight line? Instead it should be conceived as the line weaving a fractal? Unfolding in near infinite trajectories, laid out in layers upon layers, closely knit, infinitesimally thin onion-like skins, barely touching each other unraveling into infinite fractal or fractional dimensions? Infinities reminiscent of the infinities that lies between two integer numbers?
Distance, what measures the length of space between objects, looses its meaning? Distance, as we experience it in the macroscopic world, and the distance to the microscales, both work in the same way? Provide continuity for our minds to perceive? A fundamental process of our minds with distance, and therefore length, space, being the products? Emergent products?
For any effect, the world we live in, the reality for us, might unravel in infinite fractal dimensions inside thin sheets, as thick as A4 paper.
Italicized journey of thoughts, emanated by naive observations badly, anything but eloquently, expressed but nevertheless building towards new perspectives in my mind, as I gradually assimilate, (my very own meaning construction process), informed, worked-out assumptions presented by experts in the field
Heck! I forgot about that. The four blinking lights in two rows and two columns, (a matrix(?)), a rectangle near square, surrounding a two-digit number display(?). Alternate blinking of the lights per row. The two lights lying on a row were lit at the same time. One time interval, 1 time-step, then off. In the next time-step, the lights in the other row were lit, then off. Alternate lighting up per row continuously. The lights, as looked from afar gave the impression of a light running up and down. The perception of a single(!)... (the whole(?)) light jumping up and down incessantly. The lights, as being looked at, from near, did not give the impression of a running light, instead each single light in the row was constantly switched on and off. The illusion or perception of a running light, a shining beam going up and down, only given by the lights looked at from afar, but not when looked at from near. Distance of the lights from the observer being crucial? For the illusion of a running light(!) to be perceived by the observer.
Light, transmitted as waves. In both cases by different sources, but the distance from the observer would make a difference in its perception. What it is perceived. In my mind, this is how waves are perceived in our minds, and by that reality. Distance being crucial in the way waves are perceived. It is connected with perceived coherence and our ability to distinguish between simultaneously emitted waves. It is what I dealt with, as well, after I read this article about the human resolving time.
Anyhow, it evades me at the moment, but the thought that occurred to me, is connected with the microscopic world, the world of quanta.
Oumf, space being an emergent phenomenon? There is no actually space, we do not really probe space, as it is not there? It emerges as a result of the processes involved. That even flat, let's call it space, is sufficient to describe it as. The branes, to use a word from string theory, a flat surface that contains or includes, all our universe. The onion with its laid-out skins of fractal universes?
And to go back to the idea of distance being crucial to how we perceive incoming waves. Waves from atomic and sub-atomic particles, quanta for that matter, as they are perceived by virtue of the energy, they emit; in waves, each by itself a unique, single source, but what we experience, by virtue of a function(?) that combines all these waves to the reality perceived? As it emerges as reality?
And where the waves come from? They come from a distance quite afar and that's why we perceive them as running or interacting with one another.
A distance that increases as we go deeper and deeper into the microscopic world? which even creates the impression of interaction?
Interference of the waves, which we mistake as motion?
Distance, as it is experienced in the classical world and distance, by which, out of the quanta, the packets emitted, we perceive the world as is?
(in a manner analogous to combined?)
That all reality can be explained by looking at it from that angle, distance; distance from the observer, the human individual. To begin with there is the quanta, packets of energy, waves. As the waves are dispatched in packets, effectively blink, incessantly, and the observer which senses these processes from a distance; far far away; namely the distance to the microscales, to Planck length itself. A distance so remote and yet so close? The observer surmises continuity out of the stream of packets, and by that reality?
How can that happen?
Distance should not be conceived as a straight line? Instead it should be conceived as the line weaving a fractal? Unfolding in near infinite trajectories, laid out in layers upon layers, closely knit, infinitesimally thin onion-like skins, barely touching each other unraveling into infinite fractal or fractional dimensions? Infinities reminiscent of the infinities that lies between two integer numbers?
Distance, what measures the length of space between objects, looses its meaning? Distance, as we experience it in the macroscopic world, and the distance to the microscales, both work in the same way? Provide continuity for our minds to perceive? A fundamental process of our minds with distance, and therefore length, space, being the products? Emergent products?
For any effect, the world we live in, the reality for us, might unravel in infinite fractal dimensions inside thin sheets, as thick as A4 paper.
Wednesday, 3 December 2008
Quantum computers, the panacea of computing. What about chaotic computers?
Threads triggers
- The 25 Questions about Physics for the Next 25-30 Years
- The parallels of quantum phenomena and consciousness?
- Fractal Neurodynamics and Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics
- Currently phenomenally out-worldly notions
I read in The 25 Questions about Physics for the Next 25-30 Years
"15 - The understanding of complexity in computing:
Is there something beyond the artifacts of approximations ...
16 - The construction of a quantum computer:
One with 10,000 qbits would be useful; Can we construct such a real QC .."
Quantum computer? Is there not one already? Looking for a quantum computer, but what about a chaotic computer? Chaotic computer? What? Playing with words? What kind of computer would that be? A computer that his architecture is built upon the tenets of chaos? If the word tenets, as regards to chaos make any sense. What are these tenets? Attributes or properties attached to the concept of chaos. That, what the word chaos, would bring forth in an individual's mind. What kind of thoughts would be triggered upon hearing the word chaos. It certainly is, the influence of the minute, the infinitesimal quantity upon the state presented or emerging. State presented or emerging being the output and the minute or infinitesimal, the input. And what chaos dictates about the potential influence of the minute and infinitesimal upon the emergent state, the output? It is down to the sensitive dependence on the initial conditions.
Initial conditions algorithmically determined, chipped, part of the computer hardware, upon which the selection would be based, which among the minutiae of states, would be the input which will compute the output, the emergent state.
Fractal computer architecture based on registers where values representing input states, are tested against the initial conditions algorithms, the more the fractal branches, the more of the minutiae input states can be tested. Or even, by breaking up the initial conditions algorithms into smaller ones, super/sub hierarchical levels, based on a kind of AND, OR, XOR or other gate configuration available, would increase ... the 'fractality'?
Increase in complexity? Fractal branches in several levels, all being placed in such a way that the lowest registers, fed with the input values, are directly linked to the highest level registers, carrying the values which will compute for the output states? And ensure an exponential or other increase of the population of minutiae that are tested against the initial conditions algorithms?
Initial conditions based on the problem, in seek of a solution? Reverse engineering of the chaotic processes involved? What about the other tenets of chaotically developed systems. Attractors and Lyapunov exponents, diverging and converging trajectories. Can they be incorporated in the fractal architecture, be part of the initial conditions algorithms, tweak the sensitivity sought for, in the initial conditions?
In my mind, all these thoughts follow up the blueprint of the brain, in ways that have been dealt with, in Genesis of Eden paper on Fractal Neurodynamics and Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics
"The four levels of instability link in stages, making it possible for the fractal aspect of chaotic dynamics at the global, cellular, synaptic and molecular levels to combine to provide a fractal model in which global and quantum instabilities are linked by mutual interactions of scale. Global instabilities in brain dynamics may be dynamically-linked to fluctuation of a critical neuron."
The critical neuron, representing the neuron that sensitively responds to given initial conditions, fractally connected, affects the global state of the brain, the output which determines what is perceived or conceived.
In the same post, it is mentioned
"21 - Could a computer become a creative physicist:
When will this happen; How will we train them;"
A chaotic computer built out of the blueprint of the brain, might?
- The 25 Questions about Physics for the Next 25-30 Years
- The parallels of quantum phenomena and consciousness?
- Fractal Neurodynamics and Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics
- Currently phenomenally out-worldly notions
I read in The 25 Questions about Physics for the Next 25-30 Years
"15 - The understanding of complexity in computing:
Is there something beyond the artifacts of approximations ...
16 - The construction of a quantum computer:
One with 10,000 qbits would be useful; Can we construct such a real QC .."
Quantum computer? Is there not one already? Looking for a quantum computer, but what about a chaotic computer? Chaotic computer? What? Playing with words? What kind of computer would that be? A computer that his architecture is built upon the tenets of chaos? If the word tenets, as regards to chaos make any sense. What are these tenets? Attributes or properties attached to the concept of chaos. That, what the word chaos, would bring forth in an individual's mind. What kind of thoughts would be triggered upon hearing the word chaos. It certainly is, the influence of the minute, the infinitesimal quantity upon the state presented or emerging. State presented or emerging being the output and the minute or infinitesimal, the input. And what chaos dictates about the potential influence of the minute and infinitesimal upon the emergent state, the output? It is down to the sensitive dependence on the initial conditions.
Initial conditions algorithmically determined, chipped, part of the computer hardware, upon which the selection would be based, which among the minutiae of states, would be the input which will compute the output, the emergent state.
Fractal computer architecture based on registers where values representing input states, are tested against the initial conditions algorithms, the more the fractal branches, the more of the minutiae input states can be tested. Or even, by breaking up the initial conditions algorithms into smaller ones, super/sub hierarchical levels, based on a kind of AND, OR, XOR or other gate configuration available, would increase ... the 'fractality'?
Increase in complexity? Fractal branches in several levels, all being placed in such a way that the lowest registers, fed with the input values, are directly linked to the highest level registers, carrying the values which will compute for the output states? And ensure an exponential or other increase of the population of minutiae that are tested against the initial conditions algorithms?
Initial conditions based on the problem, in seek of a solution? Reverse engineering of the chaotic processes involved? What about the other tenets of chaotically developed systems. Attractors and Lyapunov exponents, diverging and converging trajectories. Can they be incorporated in the fractal architecture, be part of the initial conditions algorithms, tweak the sensitivity sought for, in the initial conditions?
In my mind, all these thoughts follow up the blueprint of the brain, in ways that have been dealt with, in Genesis of Eden paper on Fractal Neurodynamics and Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics
"The four levels of instability link in stages, making it possible for the fractal aspect of chaotic dynamics at the global, cellular, synaptic and molecular levels to combine to provide a fractal model in which global and quantum instabilities are linked by mutual interactions of scale. Global instabilities in brain dynamics may be dynamically-linked to fluctuation of a critical neuron."
The critical neuron, representing the neuron that sensitively responds to given initial conditions, fractally connected, affects the global state of the brain, the output which determines what is perceived or conceived.
In the same post, it is mentioned
"21 - Could a computer become a creative physicist:
When will this happen; How will we train them;"
A chaotic computer built out of the blueprint of the brain, might?
Labels:
chaotic computers,
fractality,
quantum computer
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