'Special Relativity' by A.P. French, Chapter 3 'Einstein and the Lorenz-Einstein transformations', p. 63.
" .. -that nature would apparently yield up no information about our state of motion with respect to a supposed fundamental frame of reference."
.. in that sentence connected, information, state of motion, frame of reference.
Information, the stuff that concepts are build out with, concepts in-turn materialise, instantiate reality, responsible for the state of motion, how nature unfolds within the bounds of frames of reference. A sentence that ties up, in a specific, dare say unique way, these three entities: information, state of motion, frame of reference.
Specific, unique way, out of the myriad (ignorance exacerbates imagination) ways available for information to be tied up, only a few combinations are allowed, survive to become the stuff for concepts, concepts that define reality, depict the way nature materialises. Information a fundamental entity that each minute detail of its existence, of its state of motion in all frames of reference brings forth. Information as conveyed in all manners of media, for all possible states, but what matters more, for information to assume its fundamental status, is to become the stuff to build the concepts that reality adheres to, is woven out of.
A notion that comes out from the processes involved in generating concepts by conversations,as it is mentioned in SCHOOLS AND EDUCATION :: LEARNING AND TEACHING, VII Conference of Foundation 2020, Thursday, 15 March 2007, Hotel Regent Esplanade, Zagreb, Education in Mind – Mind in Education: An Invitation to A Conversation. Graham Barnes, Chapter 'Education: A Story', p.16
"We constitute our concept of education (or any other concept)
(1) through conversations,
(2) in which concepts or procedures are shared,
(3) through sharing these concepts we apply them.
(4) our application of a concept creates a context, and applying a concept as a procedure produces a product. The context or product is relevant to the concept for the participant(s) who find meaning in the context.
(5) conversations are between participants but the participants are not necessarily, and are certainly not limited to, individual persons as the participants are also concepts. The participants in the conversation as concepts are also constituted by the conversation."
Concepts, as they are applied create a context, the frame of reference, produce a product. The context or product being relevant to the concept by virtue of the meaning it confers, when applied. And what comes out of, when participants in conversations are thinking about concepts, is that concepts are participants also. Concepts are thinking too, what ties human consciousness with nature. The meaning sought out by individuals when thinking the concepts inextricably tied up with the way nature is.
Concepts, in all their manifestations, propositions, theories, axioms, laws, in all the various ways they are used for, to indicate or prove or lead to, employed in thinking, the process that emulates nature's workings, guides our consciousness. It achieves its full potential when individuals make use of chaotic processes entrenched deep into our brains. Where nothing is overlooked, no bit of information possessed or coming across, is irrelevant or insignificant, and coupled with its exponential non-linear mode of being applied, lead to radical overhauls in conceptualising effortlessly.
Able to guide the mind to the right information amidst the penumbrae, seemingly disorganised bits of information, chaos apparent, and out of the penumbrae into brand new insights.
Tuesday, 29 December 2009
Thursday, 17 December 2009
Crisis induced sudden death of chaotic attractors ... Contemplating.
I read the abstract of the paper "Multiple attractors and crisis route to chaos in a model food-chain" by Ranjit Kumar Upadhyay, of the Department of Applied Mathematics, Indian School of Mines ,Dhanbad 826 004, Jharkhand, India published in the journal Chaos, Solitons & Fractals, intrigued my senses, contemplated upon its contents, and the thoughts sparked in my mind, I laid them down as they occurred, as I read through the abstract, line-by-line.
"An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range ..
narrow parameter range .. the existence of chaos in narrow parameter range .. narrow signifying the small change necessary for chaos to exist .. existence of chaos.
The notion of existence of chaos, is new to me. Is it a way to describe chaos, occurring? It seems as it is extending the properties of chaos, or may be it is better to refer to as extending the concept of chaos.
Whatever, in that particular mention, significant is the reference to a mechanism. The mechanism that is responsible for bringing into existence after, well narrowly manipulating a given connected or attached parameter range. Or, maybe just, parameter. The existence of chaos, a result of manipulating or adjusting the parameter within a narrow range. Values given of the parameter fall into a narrow stretch of the parameter's total possible range of values.
in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out.
ecological model food-chain .. a situation likely to be seen in terrestrial ecosystems
The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors.
'chaos existence caused' .. 'by crisis-induced sudden death of chaotic attractors' .. profound notion. First, is the statement, the best way I can put it, sudden death of chaotic attractors. Which, come to think of it, it accurately puts in the right perspective. Attractors, which, weight added, they are chaotic, their origin is chaos too, suddenly die. Suddenly die. Cease to exist. For chaos being dynamic, it postulates, if that term is correct, the necessity of what brought them into existence, in the first place. For the attractors to die, meaning, they lack of what they were fed with, what sustained them. What was necessary for their existence. Once, the condition that was keeping them alive, cease to be, they ceased to be, too.
That what was brought, was induced by a crisis. And their sudden death caused chaos. The existence of chaos, in narrow parameter range. Minute changes in the parameters involved brought chaos into existence. One would assume that this fresh bout of chaos would lead to new chaotic attractors. Chaos, let's say, methodology.
Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics.
'critical parameters' .. implying sensitive dependence situations. In order to identify the result, each of the crucial parameters have, in the overall state of the system, the referred to, as dynamical behaviour, you vary one at a time. Monitoring the changes, varying one of the critical parameters, brings forth. 'Fixing the regimes', what combinations of critical parameters, combined values within their ranges, that exhibit chaotic dynamics, in the sense that certain regimes are more chaotic than others. As, they would be regimes, where the system exhibits no, behaviour at all, by taking behaviour to mean, the tendency for changes, among the members of a population. If, there are no changes, there is no behaviour to speak of, and with the sudden death of the already existing chaotic attractors, there is nothing to keep the system alive. Extinction follows.
Which points towards the realisation that its submersion into chaos, is vital, in order to keep the system alive, to avoid extinction.
The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain.
'computed bifurcation diagrams' .. 'basin boundary calculations' .. bifurcations induced by crisis, test the boundaries of the attracting basins. Basins, within which, the chaotic attractors reside, and once these boundaries are surpassed, chaotic attractors can sustain themselves no-more. Their purpose ends, the system requires to spring up, rejuvenate itself, if not, the members of the population, in crisis, will perish along with the death of their attractors that was keeping them alive. Chaos is necessary for their survival.
We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a1=1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation.
'saddle-node bifurcation', 'created an unstable periodic orbit' .. unstable, there is no consistency, its trajectory changes between runs, cause a crisis manifesting at the boundaries, the chaotic attractors disintegrates. It is destroyed. As it occurs when a parameter acquires a specific value. An instability embedded in the system as the parameter fluctuates beyond its allowed range. The range that was necessary to keep the system stable, by keeping the periodic orbits stable.
Multiple attractors with riddled basins and fractal boundaries are also observed.
riddled basins, no clear-cut basins with fractal boundaries, many attractors, chaotic states, unstable
If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation.
Perturbations push the systems into the basin of a new attractor. Perturbations brought forth by epidemics or environmental catastrophes.
Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable."
"An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range ..
narrow parameter range .. the existence of chaos in narrow parameter range .. narrow signifying the small change necessary for chaos to exist .. existence of chaos.
The notion of existence of chaos, is new to me. Is it a way to describe chaos, occurring? It seems as it is extending the properties of chaos, or may be it is better to refer to as extending the concept of chaos.
Whatever, in that particular mention, significant is the reference to a mechanism. The mechanism that is responsible for bringing into existence after, well narrowly manipulating a given connected or attached parameter range. Or, maybe just, parameter. The existence of chaos, a result of manipulating or adjusting the parameter within a narrow range. Values given of the parameter fall into a narrow stretch of the parameter's total possible range of values.
in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out.
ecological model food-chain .. a situation likely to be seen in terrestrial ecosystems
The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors.
'chaos existence caused' .. 'by crisis-induced sudden death of chaotic attractors' .. profound notion. First, is the statement, the best way I can put it, sudden death of chaotic attractors. Which, come to think of it, it accurately puts in the right perspective. Attractors, which, weight added, they are chaotic, their origin is chaos too, suddenly die. Suddenly die. Cease to exist. For chaos being dynamic, it postulates, if that term is correct, the necessity of what brought them into existence, in the first place. For the attractors to die, meaning, they lack of what they were fed with, what sustained them. What was necessary for their existence. Once, the condition that was keeping them alive, cease to be, they ceased to be, too.
That what was brought, was induced by a crisis. And their sudden death caused chaos. The existence of chaos, in narrow parameter range. Minute changes in the parameters involved brought chaos into existence. One would assume that this fresh bout of chaos would lead to new chaotic attractors. Chaos, let's say, methodology.
Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics.
'critical parameters' .. implying sensitive dependence situations. In order to identify the result, each of the crucial parameters have, in the overall state of the system, the referred to, as dynamical behaviour, you vary one at a time. Monitoring the changes, varying one of the critical parameters, brings forth. 'Fixing the regimes', what combinations of critical parameters, combined values within their ranges, that exhibit chaotic dynamics, in the sense that certain regimes are more chaotic than others. As, they would be regimes, where the system exhibits no, behaviour at all, by taking behaviour to mean, the tendency for changes, among the members of a population. If, there are no changes, there is no behaviour to speak of, and with the sudden death of the already existing chaotic attractors, there is nothing to keep the system alive. Extinction follows.
Which points towards the realisation that its submersion into chaos, is vital, in order to keep the system alive, to avoid extinction.
The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain.
'computed bifurcation diagrams' .. 'basin boundary calculations' .. bifurcations induced by crisis, test the boundaries of the attracting basins. Basins, within which, the chaotic attractors reside, and once these boundaries are surpassed, chaotic attractors can sustain themselves no-more. Their purpose ends, the system requires to spring up, rejuvenate itself, if not, the members of the population, in crisis, will perish along with the death of their attractors that was keeping them alive. Chaos is necessary for their survival.
We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a1=1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation.
'saddle-node bifurcation', 'created an unstable periodic orbit' .. unstable, there is no consistency, its trajectory changes between runs, cause a crisis manifesting at the boundaries, the chaotic attractors disintegrates. It is destroyed. As it occurs when a parameter acquires a specific value. An instability embedded in the system as the parameter fluctuates beyond its allowed range. The range that was necessary to keep the system stable, by keeping the periodic orbits stable.
Multiple attractors with riddled basins and fractal boundaries are also observed.
riddled basins, no clear-cut basins with fractal boundaries, many attractors, chaotic states, unstable
If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation.
Perturbations push the systems into the basin of a new attractor. Perturbations brought forth by epidemics or environmental catastrophes.
Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable."
Friday, 6 November 2009
Understanding what mass is, in view of expanding space.
Weird notions come into my mind and I like to ponder on them and see to where they take me.
Universe expanding with the speed of light, as is mentioned here too, space expanding.
Outer space? The space between galaxies and stars or all space? Even to the space we occupy ourselves. Blowing up, expanding like balloons in all three dimensions.
It is space itself that expands, is found in NASA's Imagine the universe website,
".. but actually it is space itself that is expanding faster than the speed of light, driving objects further apart at an increasing rate."
The example of raisins in a cake as it is baked and raised up, the raisins on the surface grow distant from one another, but the raisins themselves are built on space, the concept of space is not limited only to the space observed by an individual, but includes as well the space the individual itself occupies, the raisins themselves occupy, even the space their atoms occupy.
The atom built by protons and neutrons enclosed in the nucleus and far far away, in relative terms, the electrons orbiting, an enormous amount of space included and include the point-like entities of electrons, protons and neutrons, attributed with mass equals energy, that space that lies within objects expands too, and expands with the speed of light, or, as it is claimed faster than the speed of light, in order to compensate for the ultimate speed, the speed of light, the limit all objects in the universe can be accelerated to.
We ourselves, as objects of this universe expand in space, or the space that our atoms occupy expand with or faster than the speed of light.
And all done equally, we are none the wiser. The only thing that changes is the distribution of energy in space. Which in a sense is diluted. How this notion would accommodate all what we think about what mass is? Inertial mass, rest mass of a body for zero speed; at any other speed the inertial mass is greater.
According to the equations of special relativity the mass of a body increases as it is gaining speed, it is about three times as much of the inertial mass for speeds at 0.95 of the speed of light and the graphs point to infinite mass as it gets nearer and nearer to the speed of light, asymptotic curve that never touches the y axis as the speed increases to ridiculous decimal increments to the speed of light.
What if space, all around the universe environs expands at the same time? Would an infinite mass postulate still hold? Would the beginnings of the universe from a singularity, an infinitesimal point of infinite energy be more plausible? Energy and space fundamental entities that combining the two together to produce mass? Mass an emergent entity, an entity that becomes apparent only if it is looked at from above a threshold, a macro-threshold, our familiar macro-world loosing completely that attribute when it is looked at from a point below that threshold. Mass concept becomes meaningless from the standpoint of the micro-world, the quantum realm, being only extremely concentrated foci of enormous amounts of energy kept apart by even greater distances of empty space?
What difference would that make if we take the point that this space expands at the speed of light in the same way that the universe itself expands at the speed of light.
Universe expanding with the speed of light, as is mentioned here too, space expanding.
Outer space? The space between galaxies and stars or all space? Even to the space we occupy ourselves. Blowing up, expanding like balloons in all three dimensions.
It is space itself that expands, is found in NASA's Imagine the universe website,
".. but actually it is space itself that is expanding faster than the speed of light, driving objects further apart at an increasing rate."
The example of raisins in a cake as it is baked and raised up, the raisins on the surface grow distant from one another, but the raisins themselves are built on space, the concept of space is not limited only to the space observed by an individual, but includes as well the space the individual itself occupies, the raisins themselves occupy, even the space their atoms occupy.
The atom built by protons and neutrons enclosed in the nucleus and far far away, in relative terms, the electrons orbiting, an enormous amount of space included and include the point-like entities of electrons, protons and neutrons, attributed with mass equals energy, that space that lies within objects expands too, and expands with the speed of light, or, as it is claimed faster than the speed of light, in order to compensate for the ultimate speed, the speed of light, the limit all objects in the universe can be accelerated to.
We ourselves, as objects of this universe expand in space, or the space that our atoms occupy expand with or faster than the speed of light.
And all done equally, we are none the wiser. The only thing that changes is the distribution of energy in space. Which in a sense is diluted. How this notion would accommodate all what we think about what mass is? Inertial mass, rest mass of a body for zero speed; at any other speed the inertial mass is greater.
According to the equations of special relativity the mass of a body increases as it is gaining speed, it is about three times as much of the inertial mass for speeds at 0.95 of the speed of light and the graphs point to infinite mass as it gets nearer and nearer to the speed of light, asymptotic curve that never touches the y axis as the speed increases to ridiculous decimal increments to the speed of light.
What if space, all around the universe environs expands at the same time? Would an infinite mass postulate still hold? Would the beginnings of the universe from a singularity, an infinitesimal point of infinite energy be more plausible? Energy and space fundamental entities that combining the two together to produce mass? Mass an emergent entity, an entity that becomes apparent only if it is looked at from above a threshold, a macro-threshold, our familiar macro-world loosing completely that attribute when it is looked at from a point below that threshold. Mass concept becomes meaningless from the standpoint of the micro-world, the quantum realm, being only extremely concentrated foci of enormous amounts of energy kept apart by even greater distances of empty space?
What difference would that make if we take the point that this space expands at the speed of light in the same way that the universe itself expands at the speed of light.
Labels:
expanding space,
mass
Tuesday, 25 August 2009
Systems adiabatic? Understanding subsystem-system interactions.
It is mentioned in page 166, of the book Experimental techniques in low-temperature physics by Guy Kendall White, Philip J. Meeson
"Most properties of materials are categorised in terms of the phonon system, the electron system and the spin system (i.e. the nuclear or electronic magnetic moments)."
Three subsystems that make up for most of the properties of materials, the physical and chemical properties, matter organised into the macroscopic system of the physical world, determine how the physical world behaves.
"These different subsystems, although intimately mixed together in any one material, can be separated in the imagination and analysed as independent systems."
Determine physical behaviour as the embedded sub-systems are intimately mixed, which brings into mind attractors and synchronization, attractors achieved by the ever so slight tweaking of relevant parameters, the electron-phonon interactions synchronized, by even the transient fluctuation enhancement referred to as peculiar to macroscopic systems, triggered by the exposure to additional parametres brought in, by the other embedded sub-systems.
These three subsystems separated and analysed independently? Their connections severed, each one imagined on itself? An approach which can be followed on all subsystems, lower-dimensional systems embedded in higher dimensional systems, the macroscopic systems? Understanding the relationships between embedded and embedding systems, all systems in all realms, portable via the self-similarity principle of chaos.
And all the while, each sub-system being dynamic, ever so 'touchy' to any changes introduced by either sub-system, via the electron-phonon interaction.
"Consider for example the separation of the phonon system from the electron system in a metal. This proceeds from the knowledge that the phonon system is 'heavy' arising from the motion of ions in the lattice whilst electrons are light. The mass difference (and differing statistics) influences the available energy levels in each system and ultimately limits the flow of momentum and energy between the two systems."
The phonon system 'heavy', the electron system 'light' a matter of size. The phonon system arises from the motion of ions, the electron system from electrons. This mass difference limits the flow of momentum and energy between the two systems, practically isolated from one another, each system with its own agent, phonon electron, interactions between their agents determine their behaviour.
Accordingly, it can be assumed that any introduction of extra agents, like nanoparticles upsets this balance, the flow of momentum and energy, between the two systems, as the mass of the nanoparticles being similar in size, could introduce novel interactions, leading to the emergence of properties, alien to the subsystems. The observation of novel chemical and physical properties in nanoparticles, when introduced into the nanoscales, indicative of this process.
"This 'adiabatic' or Born-Oppenheimer approximation regards the two subsystems as separate but interacting via an electron-phonon interaction."
Embedded sub-systems separate but interacting via an electron-phonon interaction? Interacting as sub-systems? Preserving their integrity, their independence of a sort. An adiabatic boundary, a barrier that prevents the direct flow of energy and momentum from an embedded system to another or even the embedding macroscopic system apart from the electron-phonon interaction, each sub-system the 'whole' by itself and as a whole interacts.
Embedded sub-systems adiabatic. Embedding systems, by virtue of being embedded themselves, sub-systems to higher dimensional systems, adiabatic too. All systems adiabatic. Biological, emotional, psychological, social systems adiabatic? Understanding systems by using the adiabatic system property?
"Most properties of materials are categorised in terms of the phonon system, the electron system and the spin system (i.e. the nuclear or electronic magnetic moments)."
Three subsystems that make up for most of the properties of materials, the physical and chemical properties, matter organised into the macroscopic system of the physical world, determine how the physical world behaves.
"These different subsystems, although intimately mixed together in any one material, can be separated in the imagination and analysed as independent systems."
Determine physical behaviour as the embedded sub-systems are intimately mixed, which brings into mind attractors and synchronization, attractors achieved by the ever so slight tweaking of relevant parameters, the electron-phonon interactions synchronized, by even the transient fluctuation enhancement referred to as peculiar to macroscopic systems, triggered by the exposure to additional parametres brought in, by the other embedded sub-systems.
These three subsystems separated and analysed independently? Their connections severed, each one imagined on itself? An approach which can be followed on all subsystems, lower-dimensional systems embedded in higher dimensional systems, the macroscopic systems? Understanding the relationships between embedded and embedding systems, all systems in all realms, portable via the self-similarity principle of chaos.
And all the while, each sub-system being dynamic, ever so 'touchy' to any changes introduced by either sub-system, via the electron-phonon interaction.
"Consider for example the separation of the phonon system from the electron system in a metal. This proceeds from the knowledge that the phonon system is 'heavy' arising from the motion of ions in the lattice whilst electrons are light. The mass difference (and differing statistics) influences the available energy levels in each system and ultimately limits the flow of momentum and energy between the two systems."
The phonon system 'heavy', the electron system 'light' a matter of size. The phonon system arises from the motion of ions, the electron system from electrons. This mass difference limits the flow of momentum and energy between the two systems, practically isolated from one another, each system with its own agent, phonon electron, interactions between their agents determine their behaviour.
Accordingly, it can be assumed that any introduction of extra agents, like nanoparticles upsets this balance, the flow of momentum and energy, between the two systems, as the mass of the nanoparticles being similar in size, could introduce novel interactions, leading to the emergence of properties, alien to the subsystems. The observation of novel chemical and physical properties in nanoparticles, when introduced into the nanoscales, indicative of this process.
"This 'adiabatic' or Born-Oppenheimer approximation regards the two subsystems as separate but interacting via an electron-phonon interaction."
Embedded sub-systems separate but interacting via an electron-phonon interaction? Interacting as sub-systems? Preserving their integrity, their independence of a sort. An adiabatic boundary, a barrier that prevents the direct flow of energy and momentum from an embedded system to another or even the embedding macroscopic system apart from the electron-phonon interaction, each sub-system the 'whole' by itself and as a whole interacts.
Embedded sub-systems adiabatic. Embedding systems, by virtue of being embedded themselves, sub-systems to higher dimensional systems, adiabatic too. All systems adiabatic. Biological, emotional, psychological, social systems adiabatic? Understanding systems by using the adiabatic system property?
Thursday, 20 August 2009
Low-dimensional systems embedded in macroscopic systems. Enhanced fluctuations?
I feel I have stumbled once again onto something which will augment my knowledge, my perspective. It will drag me away from my current endeavours to bring me back enhanced and ready for new challenges.
Writing unhindered by any considerations deemed irrelevant for my pursuits. Enough introduction, back to the point.
Šil'nikov phenomena, are referred to, in this paper titled 'Poincaré versus Boltzmann in Šil'nikov phenomena'. It was the climax of my google searching, following terms like, subordinate Šil'nikov bifurcations, Sil'nikov-saddle-node interaction, Šil'nikov phenomena, Sil'nikov chaos.
Analyse the terms and deepen my knowledge by examining the effects, the mentioned concepts had on the knowledge already held in my reverberated neural nets and in the process ascend whatever fragments are there, and emerge in new knowledge, new ways of looking at things.
In the abstract of the paper, 'Poincaré versus Boltzmann in Šil'nikov phenomena', it mentions
"By suitable adjustment of the control parameters in a CO2 laser with feedback we show experimental evidence of Sil'nikov chaos, ..."
... control parameters, as in parameters and variables. Parameters, of which their values are considered if not unchanged, changing within a very narrow limiting and limited range, as in any fractal-making program, what you tweak ever so slightly, to get all kinds, versions of the initial fractal. Suitably adjusting the parameters, deemed as controlling in the CO2 laser. Feedback providing the iteration part, the recursiveness in function, for chaos coming.
Experimental evidence of Sil'nikov chaos? What kind of chaos is this?
It further mentions,
".. characterized by intensity pulses almost equal in shape, but irregularly separated in time."
Intensity pulses irregularly separated in time, their experimental setup signature of chaos. Irregularity signifying chaos.
"The times of return to a Poincare section are statistically spread,.."
Poincare sections traversing its flow in time, incisions right through its fractal space, revealed statistically spread times of return, the order hidden amidst chaos. Chaos generating order.
Chaos as described in mathematics, measuring fluctuations in the intensity of forces, stresses, pressures plotted into graphs or even plain mathematical functions, self-referential, iterated loosing themselves into chaos. Translated into all kinds of forces exhibited in all systems possible. Physical, mental, emotional, psychological, social, spiritual systems analysed in the very same way as mathematical chaos.
"... however their iteration map is one-dimensional and in close agreement with that arising from Sil'nikov theory."
The map of the iterated points is one-dimensional? All falling onto a single line? Or the map, being a function and the one-dimensional referred to, its mathematical property. And all this, .. 'in close agreement with that arising from Sil'nikov theory'.
"Thus, the iteration map of the time intervals becomes the most appropriate indicator of this chaos."
An appropriate indicator of this chaos? Sil'nikov chaos. The one-dimensional iteration map of the time intervals?
"The residual width of the experimentally measured maps is due to a transient fluctuation enhancement peculiar to macroscopic systems, which is absent in low-dimensional chaotic dynamics."
Macroscopic systems distinct from low-dimensional chaotic dynamics? Underlying systems different than systems above? Chaotic dynamics of underlying systems, systems embedded within systems above, low-dimensional as embedded systems are bound to have less dimensions, than the system they are embedded in, embedding system which includes more than one low-dimensional systems.
The transient fluctuation enhancement peculiar to macroscopic systems? Due to the influence of additional parametres a low-dimensional system is exposed to, by the other low-dimensional system(s) that together comprise the macroscopic system they are embedded in?
Each low-dimensional system compensating for the introduced parameters, tweaked. Embedded low-dimensional systems integrated and together now determine the properties, attributes, the behaviour of the macroscopic system.
My very own thoughts developing in a similar process. All systems possible, physical psychological, social developing likewise.
Writing unhindered by any considerations deemed irrelevant for my pursuits. Enough introduction, back to the point.
Šil'nikov phenomena, are referred to, in this paper titled 'Poincaré versus Boltzmann in Šil'nikov phenomena'. It was the climax of my google searching, following terms like, subordinate Šil'nikov bifurcations, Sil'nikov-saddle-node interaction, Šil'nikov phenomena, Sil'nikov chaos.
Analyse the terms and deepen my knowledge by examining the effects, the mentioned concepts had on the knowledge already held in my reverberated neural nets and in the process ascend whatever fragments are there, and emerge in new knowledge, new ways of looking at things.
In the abstract of the paper, 'Poincaré versus Boltzmann in Šil'nikov phenomena', it mentions
"By suitable adjustment of the control parameters in a CO2 laser with feedback we show experimental evidence of Sil'nikov chaos, ..."
... control parameters, as in parameters and variables. Parameters, of which their values are considered if not unchanged, changing within a very narrow limiting and limited range, as in any fractal-making program, what you tweak ever so slightly, to get all kinds, versions of the initial fractal. Suitably adjusting the parameters, deemed as controlling in the CO2 laser. Feedback providing the iteration part, the recursiveness in function, for chaos coming.
Experimental evidence of Sil'nikov chaos? What kind of chaos is this?
It further mentions,
".. characterized by intensity pulses almost equal in shape, but irregularly separated in time."
Intensity pulses irregularly separated in time, their experimental setup signature of chaos. Irregularity signifying chaos.
"The times of return to a Poincare section are statistically spread,.."
Poincare sections traversing its flow in time, incisions right through its fractal space, revealed statistically spread times of return, the order hidden amidst chaos. Chaos generating order.
Chaos as described in mathematics, measuring fluctuations in the intensity of forces, stresses, pressures plotted into graphs or even plain mathematical functions, self-referential, iterated loosing themselves into chaos. Translated into all kinds of forces exhibited in all systems possible. Physical, mental, emotional, psychological, social, spiritual systems analysed in the very same way as mathematical chaos.
"... however their iteration map is one-dimensional and in close agreement with that arising from Sil'nikov theory."
The map of the iterated points is one-dimensional? All falling onto a single line? Or the map, being a function and the one-dimensional referred to, its mathematical property. And all this, .. 'in close agreement with that arising from Sil'nikov theory'.
"Thus, the iteration map of the time intervals becomes the most appropriate indicator of this chaos."
An appropriate indicator of this chaos? Sil'nikov chaos. The one-dimensional iteration map of the time intervals?
"The residual width of the experimentally measured maps is due to a transient fluctuation enhancement peculiar to macroscopic systems, which is absent in low-dimensional chaotic dynamics."
Macroscopic systems distinct from low-dimensional chaotic dynamics? Underlying systems different than systems above? Chaotic dynamics of underlying systems, systems embedded within systems above, low-dimensional as embedded systems are bound to have less dimensions, than the system they are embedded in, embedding system which includes more than one low-dimensional systems.
The transient fluctuation enhancement peculiar to macroscopic systems? Due to the influence of additional parametres a low-dimensional system is exposed to, by the other low-dimensional system(s) that together comprise the macroscopic system they are embedded in?
Each low-dimensional system compensating for the introduced parameters, tweaked. Embedded low-dimensional systems integrated and together now determine the properties, attributes, the behaviour of the macroscopic system.
My very own thoughts developing in a similar process. All systems possible, physical psychological, social developing likewise.
Sunday, 26 April 2009
The tremendous speeds earth is traveling in space. Is gravity a classical force? Is the search for gravitational waves a futile endeavour?
In Philosophic Wonders
"The Sun and its family of planets are orbiting the galaxy at about 135 miles per second."
The solar system moves at 135 miles per second, relativity's essence. Where the hell do we draw the certainty, be so sure, letting ourselves feel peace and tranquility, when we relax bathing in the sunshine lying in oblivion, on a beach lounger. In the knowledge, that at the same time, planet earth along with us, are propelled into the vacuum of space, in shearing shattering speeds. If we subject, the hapless fragile human being, in these tremendous unreal speeds, we will be lucky to find traces of the bones to verify its past existence.
And yet, here we are, alive and well, despite the speed we travel in space, to have the arrogance to enjoy, a peaceful morning. Peaceful. Anything else apart.
Centripetal force, the essence of gravity, what keep us pinned on the ground. That do not let us, being swept away from the face of planet earth, and not only us, but what keeps the dust, the rocks on the face of the moon and all the rest of the planets and other so-called heavenly bodies.
Gravity, that sucks us inwards, towards the centre of planet earth, to spare us the oblivion of our precious being, by the shattering speeds, our very own nurturing earth, is itself subjected to.
Apart from the solar system traveling at 135 miles per second, we have as well that
"The Earth rotates on its axis at about 1,100 miles an hour, a motion that creates day and night."
and
"The Earth orbits the Sun at about 67,000 miles an hour, a motion that takes one year."
and
"The Sun circles the Milky Way at a speed of about 486,000 miles per hour."
and
"And every object in the Universe is moving apart from the other objects as the Universe expands at a constantly accelerating rate."
Devastating forces that would have left nothing standing, long enough, that not only life nurtured, in the warm and welcome abode of planets, but even the existence of these wonderful incubators, if it wasn't for the protection offered by the gravitational forces, that not only effectively counteract against the shearing power of the speeds developed, by heavenly bodies in their endless journey in the vast space but even overcomes it, for us to enjoy the tranquility of nature.
Heavenly bodies in their endless journey around the centre of... The centre of .... their very own system or any other system they are part of. Earth orbiting around itself, moon orbiting around itself and moon orbiting around earth, the earth-moon system. Earth orbiting around the sun, the planets orbiting around the sun, the solar system around... Circularity.
Driven by gravity itself and by gravity is counteracted. The shearing speeds that the motion, its very own existence propagates and as it is counteracted by, at the same time. A dependency built-in, in the system, in each system by itself, the speed and the forces developed cannot be greater, than what the heavenly body can withstand. The speed of rotation around itself, as well as around the larger body in the system, would not be allowed to reach levels that would jeopardize its very own integrity. The seemingly hazardous journey, a gentle stroll in comparison.
How can we comprehend the nature of gravity, when we think of its appearance, as it vanishes down to the centre of a heavenly body. Attraction, of every piece of matter upon each other. Additive, as more and more pieces of matter accumulate, the stronger it becomes. Heavenly bodies borne out of dust, stardust as it has been found, accumulating into foci driven by chance (chance?) ... for more and more dust particles to gather up into the heavenly bodies which they become. What they are now. Matter may be pushed into coalescing, ... by the very vacuum surrounding it ... via pressures they are subjected to. Is it just a vacuum pressure effect or an actual attraction of matter objects. The actual rotation of a heavenly body around itself, a vacuum pressure effect. The same would hold valid, regarding the rotation of a heavenly body around its bigger counterpart in the system, rendering the presumed action at a distance character meaningless, what elevates gravity from a purely classical force into a fundamental force. Is the search for the graviton justified, or even the existence of gravitational waves feasible, the search for gravitational waves a futile endeavour.
The whole case, can be thought of in terms of systems. Systems within systems, a guiding principle universal for all systems. Systems that are dynamic ...
Oh, well fractal. Is there anything apparent in the galaxy system that would justify the term fractal? May be not merely in its spatial dimensions, but taking into account its evolution through time too. Energy dissipation. Energy being apparently high, at the very centre of a galaxy, stellar nurseries, black holes. Dissipating to lower and lower energies towards its perimeter. Fractal being characterized by its non-integral nature, non-integral dimensions. Is there any indications of non-integral dimensions in the galaxial system organisation?
What about warped spacetime, wormholes and the like. Does that not point towards a fractal evolution for the galaxy system. Gravity a mere manifestation of energy dissipation governed even by the Feigenbaum series concept.
"The Sun and its family of planets are orbiting the galaxy at about 135 miles per second."
The solar system moves at 135 miles per second, relativity's essence. Where the hell do we draw the certainty, be so sure, letting ourselves feel peace and tranquility, when we relax bathing in the sunshine lying in oblivion, on a beach lounger. In the knowledge, that at the same time, planet earth along with us, are propelled into the vacuum of space, in shearing shattering speeds. If we subject, the hapless fragile human being, in these tremendous unreal speeds, we will be lucky to find traces of the bones to verify its past existence.
And yet, here we are, alive and well, despite the speed we travel in space, to have the arrogance to enjoy, a peaceful morning. Peaceful. Anything else apart.
Centripetal force, the essence of gravity, what keep us pinned on the ground. That do not let us, being swept away from the face of planet earth, and not only us, but what keeps the dust, the rocks on the face of the moon and all the rest of the planets and other so-called heavenly bodies.
Gravity, that sucks us inwards, towards the centre of planet earth, to spare us the oblivion of our precious being, by the shattering speeds, our very own nurturing earth, is itself subjected to.
Apart from the solar system traveling at 135 miles per second, we have as well that
"The Earth rotates on its axis at about 1,100 miles an hour, a motion that creates day and night."
and
"The Earth orbits the Sun at about 67,000 miles an hour, a motion that takes one year."
and
"The Sun circles the Milky Way at a speed of about 486,000 miles per hour."
and
"And every object in the Universe is moving apart from the other objects as the Universe expands at a constantly accelerating rate."
Devastating forces that would have left nothing standing, long enough, that not only life nurtured, in the warm and welcome abode of planets, but even the existence of these wonderful incubators, if it wasn't for the protection offered by the gravitational forces, that not only effectively counteract against the shearing power of the speeds developed, by heavenly bodies in their endless journey in the vast space but even overcomes it, for us to enjoy the tranquility of nature.
Heavenly bodies in their endless journey around the centre of... The centre of .... their very own system or any other system they are part of. Earth orbiting around itself, moon orbiting around itself and moon orbiting around earth, the earth-moon system. Earth orbiting around the sun, the planets orbiting around the sun, the solar system around... Circularity.
Driven by gravity itself and by gravity is counteracted. The shearing speeds that the motion, its very own existence propagates and as it is counteracted by, at the same time. A dependency built-in, in the system, in each system by itself, the speed and the forces developed cannot be greater, than what the heavenly body can withstand. The speed of rotation around itself, as well as around the larger body in the system, would not be allowed to reach levels that would jeopardize its very own integrity. The seemingly hazardous journey, a gentle stroll in comparison.
How can we comprehend the nature of gravity, when we think of its appearance, as it vanishes down to the centre of a heavenly body. Attraction, of every piece of matter upon each other. Additive, as more and more pieces of matter accumulate, the stronger it becomes. Heavenly bodies borne out of dust, stardust as it has been found, accumulating into foci driven by chance (chance?) ... for more and more dust particles to gather up into the heavenly bodies which they become. What they are now. Matter may be pushed into coalescing, ... by the very vacuum surrounding it ... via pressures they are subjected to. Is it just a vacuum pressure effect or an actual attraction of matter objects. The actual rotation of a heavenly body around itself, a vacuum pressure effect. The same would hold valid, regarding the rotation of a heavenly body around its bigger counterpart in the system, rendering the presumed action at a distance character meaningless, what elevates gravity from a purely classical force into a fundamental force. Is the search for the graviton justified, or even the existence of gravitational waves feasible, the search for gravitational waves a futile endeavour.
The whole case, can be thought of in terms of systems. Systems within systems, a guiding principle universal for all systems. Systems that are dynamic ...
Oh, well fractal. Is there anything apparent in the galaxy system that would justify the term fractal? May be not merely in its spatial dimensions, but taking into account its evolution through time too. Energy dissipation. Energy being apparently high, at the very centre of a galaxy, stellar nurseries, black holes. Dissipating to lower and lower energies towards its perimeter. Fractal being characterized by its non-integral nature, non-integral dimensions. Is there any indications of non-integral dimensions in the galaxial system organisation?
What about warped spacetime, wormholes and the like. Does that not point towards a fractal evolution for the galaxy system. Gravity a mere manifestation of energy dissipation governed even by the Feigenbaum series concept.
Friday, 24 April 2009
.. a ... significance of Lyapunov exponents? ... to absorb chaos?
... to absorb chaos?
.. a ... significance of Lyapunov exponents? In their predictive(?) power to show whether a certain trajectory converges or diverges? Convergence or divergence determining the way that chaos is viewed by individuals? Diverging pathways, or for that matter constantly diverging pathways, result in what as seen as chaos and converging pathways create attractors, which can be seen as order?
... determining a measure of Lyapunov exponents out of the processes involved which will show whether the processes undertaken will bring about order or chaos? In almost everything which evades a thorough analysis by any other prescribed procedures but exhibiting chaotic tendencies?
Rigorous mathematics, scientific proof, all part of cognition which is taking place outside, from where it should be taking place. The human mind. As meaning is derived by mind itself, it can not materialise in spheres other than what the mind provides for. And attempting to frame meaning, with processes that the language provides it is a futile endeavor, because at the end the whole process must be accepted by the mind itself.
.. a ... significance of Lyapunov exponents? In their predictive(?) power to show whether a certain trajectory converges or diverges? Convergence or divergence determining the way that chaos is viewed by individuals? Diverging pathways, or for that matter constantly diverging pathways, result in what as seen as chaos and converging pathways create attractors, which can be seen as order?
... determining a measure of Lyapunov exponents out of the processes involved which will show whether the processes undertaken will bring about order or chaos? In almost everything which evades a thorough analysis by any other prescribed procedures but exhibiting chaotic tendencies?
Rigorous mathematics, scientific proof, all part of cognition which is taking place outside, from where it should be taking place. The human mind. As meaning is derived by mind itself, it can not materialise in spheres other than what the mind provides for. And attempting to frame meaning, with processes that the language provides it is a futile endeavor, because at the end the whole process must be accepted by the mind itself.
Space, a result of forces? Interaction of forces? It is bound to be.
New thoughts light up, in my mind... Exciting.
Space, a result of forces? Interaction of forces? It is bound to be.
As all these I have been working out, put into these posts .... are getting pieced up together, become coherent.
(Regression). I have to analyse this. The way it happens. What makes a thought developed independently, loose as is, with no ties (obvious?) with any other thoughts (residing in some other realm, context). But out of no-where, without warning, nevertheless click (systems exhibiting chaos' self-similarity?), or hook, or whatever, one with the other. They become connected, tag and drag along the entirety of the concept, notion, thought, idea; the bonus being, all the rest of the properties and attributes, these mental structures, are associated with. A bonus since, as the thinking develops, all these properties and attributes, branching-like extensions on all sides, are engaged in the thinking process. Being tags themselves, either concepts, or notions, or thoughts, or ideas, potentially concise and coherent mental structures, on their own right, they have all what is needed, to form by themselves, novel associations. The word 'concepts', as it comes into mind, with their properties (as they develop), provide the associations, and by virtue of their associations, cohere from ..(humble, incoherent, haphazard) beginnings ... into more inclusive concept circa thoughts.
Space, (as I have surmised in that post) was non-existent before the big bang, or in the manner we experience it right now. (Vast, solid objects within, immense, three dimensional, containing or expressed with or give substance to the word-concepts of macrocosm and microcosms). Space, distance developed fractally the world we live in, the universe, just a thin fractally developed sheet. Space, a reference frame fractally developed, 'sitting' on another deeply fundamental space
Space, a result of forces? Interaction of forces? It is bound to be.
As all these I have been working out, put into these posts .... are getting pieced up together, become coherent.
(Regression). I have to analyse this. The way it happens. What makes a thought developed independently, loose as is, with no ties (obvious?) with any other thoughts (residing in some other realm, context). But out of no-where, without warning, nevertheless click (systems exhibiting chaos' self-similarity?), or hook, or whatever, one with the other. They become connected, tag and drag along the entirety of the concept, notion, thought, idea; the bonus being, all the rest of the properties and attributes, these mental structures, are associated with. A bonus since, as the thinking develops, all these properties and attributes, branching-like extensions on all sides, are engaged in the thinking process. Being tags themselves, either concepts, or notions, or thoughts, or ideas, potentially concise and coherent mental structures, on their own right, they have all what is needed, to form by themselves, novel associations. The word 'concepts', as it comes into mind, with their properties (as they develop), provide the associations, and by virtue of their associations, cohere from ..(humble, incoherent, haphazard) beginnings ... into more inclusive concept circa thoughts.
Space, (as I have surmised in that post) was non-existent before the big bang, or in the manner we experience it right now. (Vast, solid objects within, immense, three dimensional, containing or expressed with or give substance to the word-concepts of macrocosm and microcosms). Space, distance developed fractally the world we live in, the universe, just a thin fractally developed sheet. Space, a reference frame fractally developed, 'sitting' on another deeply fundamental space
Sunday, 29 March 2009
Higgs boson existence?
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."
"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."
Labels:
Higgs boson
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
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