In some sense what is simple is that which contains little information; what is complex, much information.

In this sense, something is simple or complex because that is the way it is.

In another sense, what is simple is what is easily understood; what is complex, understood with difficulty. Information is part of the picture. What contains more information may be more difficult to understand.

In the second sense, something is simple or complex relative to an individual animal. What is simple to one animal may be complex to another. Why that is would be a matter for psychology to investigate.

As to entropy... yes, I think entropy may be defined in terms of information. Thus there would be a connection there.

what makes complexity and simplicity in the process design vizual communication

In nature almost every thing is simple. However if we look in to the externalities it appears complex.

For example all living organisms have only four bases ATGC or U. The arrangements of these four bases (a raw material for making DNA or RNA) makes different genes at Genotypic level. Rge Phenotype of these arrangements varies considerably i.e. one will lead to emergence of Amoeba and other will make Fish (Matsya), Tortoise (Kurma), Pig or Swine (Varah), Tiger (Sinha), Dwarf man (Batuk or Waman), Man (like Ram or Ravan).

Each living organism is creating entropy to attain a newer hight of Order. The process is continuous. It wont stop. Order and disorder they help each other. You stop entropy and the universe will sink all of a sudden sois the case of order in the universe.

That is an interesting concept, that every living organism is creating entropy to attain a newer hight of Order.

But I think you are dropping into the disorder fallacy of entropy.

I personally don't subscribe to that thought, if only because entropy is simply in my lexicon the spreading of energy more thinly across the Universe. Whether a local situation has more energy or entropy, Has an impact on order, but it is not a simple one to one impact where more entropy causes more disorder, and frees up more order for the living thing.

Wolfram's 4th order cellular automata, seemed to suggest that in an incremental system, the order and chaos oscillated instead of trending in any one direction. In "Edge of Chaos" theory, it has been suggested that order precipitates out of chaos, when entropy and energy reach a certain level of balance. It can be shown that even evolution is merely a system whereby entropy is worked out for populations instead of individuals.

In this approach to science we need to understand that there is constraints on how much order can exist within a certain area, and that the constraints are part of the reason why seemingly simple things, can be analyzed into quite complex structures if they are looked at at a low enough level.

It is my contention that an ultimately simple thing, will not have relationships within it, and therefore will not be able to store information.

GS: "That is an interesting concept, that every living organism is creating entropy to attain a newer hight of Order."

Ilya Prigogine, a Nobel Prize winning chemist proposed similar ideas...

http://en.wikipedia.org/wiki/Ilya_Prigogine#Dissipative_structures_theory

Yes, Bill, although I can't say that I am familiar with his work, I have been exposed to it, in some sense.

#H1-171 sdodvo dt 1111. Ref Graeme Smith, Dec 29, 2010 12:49 pm. If you don't mind, may you please explain what is the relationship between the under-grouped?

*energy, entropy, order, disorder, balance, precipitating.

*constraint on order, spatial area, size scale.

#H1-172 sdodvo dt 1111. Ref Bill Overcamp, Dec 29, 2010 11:25 pm. I read the Pregogine link you provided. And the following are my question:

@*. i think, it is simply a case of relative velocities. We observe faster than we can explain; and that appears to us a widening gulf between us and uncertainity. But, it is still possible we may be able to outpace, given that a single theory may cover a thousand observations. Other reasons are, more people are enggaged in observing facts than in explaining them. Another reason is observation always precedes explanation in time, leaving more uncertainity open before certainity can start consider.

# May be a Noble laurate's life time work is the end of certainity, demographic factors may indeed may continue to further shift the equilibrium towards uncertainity. And i am here may be half an hour. The very audacity shall pronounce i am wasting time falling prey to overassumptions.

@* But would not certainity ask, uncertainity of what? Of necessary and/or usable universe? If of unusable dimensions, is that going to affect in the communicable presence, any necessiities or uses of life and nonlife forms, and do we understand so? If not of these, then where we can abandone certainity and embrace uncertainity as the end?

I think Ilya Prigogine's work should be understood in context. Prigogine's real accomplishments are in chemistry, not cosmology. Certainly, an open, potentially infinite universe can not be comprehended by our finite minds.

Energy is the base concept, essentially energy is the potential for action, or the action itself.

In Newtonian Physics, we talk about Force, in that the rule is that nothing changes without a force. This is taken as being the law of inertia.

In the Second Law of Thermo-dynamics we talk about Entropy, in that the second law states that nothing moves without increasing entropy.

Some physicists and mathematicians have suggested that Entropy increases with disorder, or visa versa. Some physicists and mathematicians have suggested that the system becomes more and more disordered the more entropic it is.

An example is the Shannon concept of signal disorder, or the Boltzman concept of disorder, What seems strange is that if we look at natural systems, such as steam, as we increase the entropy (Cool Down the media) it tends to co-allese into gradually more and more ordered terms, instead of tending to disorder. The assumption is that at some point it will become less ordered, by breaking the bonds between the higher ordered elements.

Ok, so if we look at energy, we find a rule that states, energy flows to the least potential. Thus heat flows from hot places to cool places, and electricity flows from high voltage to low. It is my belief that this describes the "Flip Side" of Entropy, in that as the energy flows from an object the "Entropy" increases.

GS: "Energy is the base concept, essentially energy is the potential for action, or the action itself."

In my humble opinion, energy does not exist in any primary sense, but is a mere property of substance, having no independent existence apart from substance. That this is so can be seen from the fact that scientists use the term, 'energy,' equivocally, to refer to essentially different things. Kinetic energy is ascribed to moving substances. Potential energy is ascribed to substances for several different reasons. Thus we speak of energy stored as heat, or in a spring, or in a gravitational or electrostatic field. Energy itself, is not measured directly, but is calculated through different formulæ in different situations.

Energy is important in physics only because it is conserved. It is an interesting question how something which does not exist substantially can be conserved. The only answer I can give is that the world is designed that way.

GS: "In Newtonian Physics, we talk about Force, in that the rule is that nothing changes without a force. This is taken as being the law of inertia."

Wrong... Movement, a sort of change, does not require force. Acceleration and deceleration require force. F=MA. No acceleration (or deceleration) means no force is acting. But change does not necessarily involve acceleration or deceleration.

GS: "In the Second Law of Thermo-dynamics we talk about Entropy, in that the second law states that nothing moves without increasing entropy."

Wrong... Movement does not increase entropy... except accidentally by way of friction.

From what I understand, the laws of thermodynamics are essentially unrelated to the laws of motion. Some have tied them to the law of large numbers, but it explains nothing physically... being a purely statistical relationship. I would suspect that the ultimate explanation for the laws of thermodynamics depends on Quantum Mechanics and the Uncertainty Principle... things which can not be derived from the laws of motion.

GS: "Ok, so if we look at energy, we find a rule that states, energy flows to the least potential. Thus heat flows from hot places to cool places, and electricity flows from high voltage to low. It is my belief that this describes the 'Flip Side' of Entropy, in that as the energy flows from an object the 'Entropy' increases."

I know of no such 'law.' I'm not even sure what you mean by 'least potential' in that context. Certainly your examples, high versus low voltage, high temperature versus low temperature represent vastly different phenomena. It is hard to see some law common to those situations. Does this law have a name?

Oh, Bill, sometimes you amuse me.

Let me describe the inertial frame for you:

When-ever an object is in motion it shall remain in motion, and when-ever an object is at rest it shall remain at rest unless operated upon by a force.

In other words in the inertial Frame, continuing to move on the same trajectory, is not considered change, but status quo.

"Movement does not increase Entropy - except accidentally by way of friction"

In my definition of entropy as the spreading of energy from locations of high potential to areas of low potential any moving object acts as a carrier of energy, and the net effect of all movement is to spread energy over a wider area. Think of the "Momentum" of the object as being potential energy, when it eventually reaches another object, and impacts, it will transfer the energy of movement to that other object, in essence increasing entropy as a result.

"I know of no such law" sure you do, it is just that you think that the law speaks about something else, the law is called Entropy. And one of the reasons that it represents such widely different phenomena, is that it is ubiquitous in an Energy/Entropy based Universe. There is nothing that is not effected by Entropy. Including I dare say God.

The terms 'high voltage' and 'low voltage' are somewhat ambiguous. Of two potentials, -1000 volts, and +5 volts, which is the higher voltage? I would suppose it would be the +5 volts. Electrons, being negatively charged, flow from the negative to the positive... from the lower voltage to the higher. 'Electron holes' in a semiconductor, being positively charged, flow from the positive to the negative, from 'higher' to 'lower.' Similar phenomena in charged liquids or gasses may involve either positive or negative ions. Thus in the electrolysis of water, hydrogen ions will flow to a negatively charged plate (the lower voltage) while oxygen ions will flow to a positively charged one (the higher voltage).

GS: "In other words in the inertial Frame, continuing to move on the same trajectory, is not considered change, but status quo."

According to Newton, motion is relative, so it involves two objects, moving relatively to each other. This is called Galilean Relativity. Thus an object sitting on the deck of a ship is not moving relative to the ship, but it is moving relative to shore.

Einstein's relativity is built on Galilean Relativity. In General Relativity, one might consider the motion of an object relative to the curvature of space.

You may not understand such relative motion as a change, but the rest of humanity does.

SG: ""I know of no such law" sure you do, it is just that you think that the law speaks about something else, the law is called Entropy. And one of the reasons that it represents such widely different phenomena, is that it is ubiquitous in an Energy/Entropy based Universe. There is nothing that is not effected by Entropy. Including I dare say God."

An interesting interpretation to be sure... Is your 'unit field' subject to entropy?

"The terms High voltage and low voltage are somewhat ambiguous"

That is why you amuse me, Bill, there is no ambiguity at all.

Voltage is always a reference of potential with respect to some reference state. I.E. it is relative to a state, usually ground, that we can measure from. So, yes it is possible for +5 volt to be a higher voltage than -10,000 volts depending on the reference point. If we assume that the reference point is ground, then the statement is obviously false since you are mistaking polarity for potential. The voltage is 10,000 volts whether or not the polarity is negative or positive. Polarity just helps us determine which side of the ground state that voltage is connected on.

In the case of the +5v supply, given a reference point of -10,000 volts, a +5 volt potential with respect to ground would define a 10,005 volt potential across the whole circuit. That is why we can put batteries together into battery packs, and merely add the voltage if they are in serial, organized negative to positive and halve the internal resistance if they are in parallel.

"According to Newton, motion is relative, so it involves two objects, moving relatively to each other. This is called Galilean Relativity."

And your point is?

Consider the statement it is not the fall that kills you, it is the stop at the bottom.

When you try to say that there is no entropic effect to movement you are saying you never stop at the bottom of a fall.

By the same token when you say that relative movement is change, (In an inertial frame) you are actually saying that because there is a reference point from which change can be said to be happening, it invalidates the inertial frame which is all about the object itself changing its direction. I don't expect you to notice that you have essentially mixed your metaphors and negated your own objections, but physically you have in fact done so. It is a simple misapplication of theory, and to be expected in someone with a purely book grasp of the subject.

Oh, and Yes, Unit Field creates energy and thus must itself be subject to entropy. In fact, it is the expansion of Unit Fields population within the Universal Field, that defines the Expansion of the Unit Field Universe, which I do not as yet state is the same as ours, if only because there is no proof, that they are more than analogs similar to each other, and this expansion of the Universe, is the seat of it's Entropic nature, in that uncertainty caused by LSG events, means that local sources of Energy, are constantly acting to perturb the Universal entropic ambient, with the result that the predictions of the Energy death of the Universe are perhaps indefinitely postponed.

So again yes, there is NOTHING that is not affected by Entropy. That is why Entropy is so hard to prove, what state can you use as a control? The best you can do, is compare local entropic effects against the Universal Ambient, in somewhat the way we compare temperature since nothing in the Universe does not have a temperature.

GS: "That is why you amuse me, Bill, there is no ambiguity at all."

OK, you are using the term as I thought you would. Suppose that a voltage source at -5 volts relative to ground is connected by a simple copper wire to a voltage source at +1000 volts relative to ground. Electrons, being negative in charge and being readily conducted by the copper wire, will flow from the low voltage to the high voltage, contradicting what you said, "electricity flows from high voltage to low."

GS: "And your point is?"

That relative motion, is a sort of change that does not involve force. Acceleration and deceleration involve force. F=MA.

Is Euclidean geometry affected by entropy? Euclidean geometry is nothing but what its axioms state. Those axioms make no reference to time or to anything affected by time.

Please note that I mean pure Euclidean geometry, not something embodied in a physical body.

If it is affected by entropy, please give me an example of a theorem which will somehow be affected by it. For example, how will the Pythagorean theorem be affected?

Suppose two astronauts are on a spacewalk. One of them jokingly tosses an object to the other, who catches it. While it is traveling between the two it is essentially unaffected by any forces and moves in a straight line from one to the other. I say that the mere motion of the object will be detected by the astronauts as change.

Now one may say that even in space there will be some friction against the near vacuum of space. I will grant that. But the affect of such minute forces will be deceleration, not mere motion.

And if one says that the relative motion is merely the 'status quo' I may even grant that, but it is still a change --- and will be perceived by the astronauts precisely as a change.

#H1-177. Ref Bill Overcamp, Jan 4, 2011 9:59 pm.

@*. If i take this as a question, it's really interesting. Does and if, how entropy may affect "ideas/concepts/theorems/propositions". How indeed?. Entropy, we said, affects beneficiation of work/energy, it requires some waste/disorder as part of any productive process. We said en ensemble is subject to it, objects are subject to it, microsopic events are subject to it, as well as cosmological events. So far it had been growing, to encompass the entire physical universe.

Now we [Bill started it!] we are asking,would there be an effect of entropy on "theorems". I wonder, if in the meaning of the theorem? Unlikely. Change in the meaning becomes the realm of genesis/growth of a theorem, so let us leave meaning alone for the present, and go to see the "development/growth of meaning/theory". Should entropy affect it.

We/i do not see any reason, how could it. But if we want to use the name, then what could be the labile characteristics vulnerable to such an allegation? The genesis/growth of a theorem, ie before it becomes a theorem, that phase is susceptible. The theorem may be thought towards, through intermediate right and wrong steps, however ultimately growing to become the theorem. These erroneous steps before a "theorem" is reached, we may attribute to "entropy"; which means, we are fastening on the thought process a kind of or partly "chance/random" reasoning; this is because, entropy is more or less accident ie unpremediable uncertainty, "too fast choosing a branching of thought", and entropy is never a constructed one or anticipatable one-to-one [or if so].

If we equate entropy to "unpremediable uncertainty" [i think uncertainty may itself may suffice, but here i add an adjective because i want to emphasize the way the uncertainty/error/entropy may originate, a "work of broken logic"; i would seem to suggest by this that all thoughts could potentially lead in the right and straight path to the theorem, but for getting "logically broken" ie "logic formation interrupted by unfinished consideration, for reasons that generally contribute to uncertainty, or some funneling effort towards comfort/unprolonged completion of the task".

So a settled theorem/meaning may not be subject to entropy, but a thought in progress may be. Or possibly, i have all along been using the concept [of entropy] too loosely, and have arrived at these and these are only errors and have no connection with uncertainty or entropy. How it is possible to subject energy(=entropy) and information(=entropy) to mere errors(dilute entropy?)?

Let that we consider later[why go to a losing cause!]. next,to the next fascinating,losing cause:

How say Pythagorean theorem will be subject to entropy. I want to simplify the question: how 1,2,3 or 1+2=3 will be subject to entropy. i am saved; i don't subscribe to any doubt [except in the realms i myself may talk of, not here, probability of 2 or 3] as to that the meanings of or unchangeability of the meanings of 1,2,+. Therefore, atleast "abstract truths" themselves as such are not subject to entropy; for that matter, anything, when changing, and whatever and whenever, when changing is subject to uncertainty/entropy.

I am so tired of this uncertainty, ihave already said in may be another thread, i want to see what is the other end of uncertainty: When uncertainty grows like crystal growth or liquid-crystal growth, what certainty can get seeded into it and what batonnet of certainty would get formed, i want to know. For this, some certain idea(theorem) should become susceptible to uncertainty and continually increasing so, and at some point uncertainty would become more, and then a next "certainty/theorem" would start precipitating out?

But is not this the usual way ideas evolve? Then am i taking so much wonder and words to reach back to the starting question, now to wonder if the question itself is superfluous?

What attractor this similar-fate is of me.

_______________________________

EDITdone. Spelling checking.

SN: "So a settled theorem/meaning may not be subject to entropy, but a thought in progress may be."

I was not asking whether mathematicians are subject to entropy. Obviously, we are. Nor am I asking about any particular thought process or habit of mind or mode of expression.

I am referring, rather to Euclid's system of axioms --- updated to reflect modern mathematical precision yet perfectly compatible with what Euclid, himself, wrote --- along with the theorems derived from that system.

Such a system is, in fact, a mere potency... something which actually exists nowhere --- not even in the mind of a mathematician --- but which can be approximated in a variety of ways.

Is that abstract potency subject to entropy?

Oh, Bill, I just got through telling you that potential has nothing to do with polarity, that voltage is a relative thing and MEASURED according to a reference point. Where in that explanation did you get the idea that the 1005 volt potential had anything to do with the DIRECTION of flow? Of course electrons always flow from negative to positive, (in standard usage) but that is because there are more electrons in the negative pole than there are in the positive one, not because we called it negative or positive. And you have completely forgotten the "Holes" that flow from positive to negative in some electronic theories because the Positive pole is high in positive ions. So if electrons were the only thing moving why does an arc welder work?

You insist on simplifying the physics to make claims that are not at all born out by physics.

So since you like to use thought experiments here is one that will blow your mind, and maybe your fuse, put your negative 1000 volts on one side of the circuit, and ground the center of the circuit, and put your +5 volts on the other side of the circuit. How much electricity will reach the +5 volts now? The answer is 5 volts or nothing, because the ground will absorb all the holes from the +5 volts, and will supply all the holes needed to absorb the full 1000 volts. But don't stand too close or your hair might get curly.

"relative motion is a type of motion that does not require force"

Right, and Santa Clause came down my chimney and kissed my mother, pull the other one do, how do you think the motion came into being? Relative motion is simply motion that is measured from a relative POV. The inertial frame has to do with the individual element and the rules by which it moves, accellerates and decelerates. Relative motion has to do with how the change in location is percieved from a different location, and does not imply any change to the inertial frame and therefore does not imply any force. There is no problem simply because you are ignoring the fact that you are switching frames.

Is Euclidean Geometery affected by entropy? Well first does Euclidean Geometry exist?

If it exists, in any form, including signals in our brain then it is affected by entropy, that does not mean that it is changed by entropy, but it might mean that we would never have thought of it, if it were not for entropy. After all thought in the human mind is dependent on chemical changes in the neuron, and chemical changes are all affected by entropy.

Its a trite point, but then this is descending into sillyness anyway.

Ok, now where on the world did you get the idea that you could throw or catch a ball without force? Ok, so we are not on the world, but in space, I hope your astronauts are wearing magnetic shoes and standing on a steel ship, because if they throw and catch a ball in space without some such protection they are going to really need to deal with unexpected consequences, not only will the ball impose its momentum on the catcher, but the momentum of the throwers arm movement will result in violent adjustments to his trajectory.

Not only that, but the trajectory it, (the ball) takes is going to be slightly different than the one that it would have taken on earth, and as a result, the catcher may not be able to reach it unless the thrower is an experienced space hand, (so to speak)

Ok so what is happening? first the thrower throws the ball, and somehow keeps his balance, the ball flys through vacuum, and the catcher catches it. What is the change? In the Inertial frame the ball is imparted with a certain amount of force, which causes it to accellerate, then it coasts at a constant velocity for a while, and then a certain amount of force causes it to decelerate, and the catcher is the one who has to keep his balance.

Ok, so in the inertial frame we have only the work needed to move the ball from one astronaut to another. The displacement is not in the intertial frame, it is in the relative frame. So it doesn't matter to inertia if there is physical displacement. Sure it matters to the astronauts especially if they are caught off guard and lose their ballance, but that only represents the force needed to first throw the ball, and then catch it. During the time it is floating in space, on the constant speed trajectory, neither astronaut is affected. What is affected is the photons that reflect off of it, and how they impinge on the eye, which is its own inertial frame and constant velocity trajectory. The catching astronaught can use the reflected photons to decide how to catch the ball, but that is outside the inertial frame again. What I complained about was not the impact of the virtual particles in space on the ball, but the shifting of frames and drawing conclusions about the inertial frame from the relative displacement in space. If you use the wrong mathematical conventions you are going to get confused, and obviously bill you are confused.

GS: "And you have completely forgotten the "Holes" that flow from positive to negative in some electronic theories because the Positive pole is high in positive ions."

I take it that you forgot that I had myself pointed out both electron 'holes' and positive ions in a previous message.

In any event, the actual flow may go from the lower voltage to the higher or vice versa, while you said... "electricity flows from high voltage to low."

GS: "how do you think the motion came into being?"

In general, that's not my problem. Perhaps your 'unit field' could just created it that way?

GS: "Well first does Euclidean Geometry exist?"

As I wrote before, it actually exists nowhere, but is an abstract potency which may be approximated in many different ways.

In any event, name a theorem which will become corrupt due to entropy.

GS: "then it coasts at a constant velocity for a while."

Exactly. It moves at a constant velocity. The astronauts perceive its position changing without there being any force applied to keep it moving. F=MA.

This clearly contradicts Aristotle who thought a projectile has to be pushed by the air as it goes.

If Euclidean Geometry Doesn't exist, how come you are talking about it? I think you are being intentionally naive, or using an overly restricted definition of exist.

Hold it, Air can't push a ball, in vacuum, but it can in Atmosphere, reference high winds, and hurricanes that put balls through windows etc.

However I admit it is not the base case, and you do not get constant velocity in air because air is always associated with gravity (On the Surface of the Earth) and so you get a trajectory that curves according to the accelleration of gravity. I assume your Astronauts are at a lagrange point and therefore have a net null gravity effect?

But whether or not there is a Force keeping it moving, the fact is that there is no reason to claim that inertia is wrong.

#H1-178. Ref Bill Overcamp, Jan 4, 2011 8:11 pm.

@*. How many entropies do i understand so far? From "unprimary use$$/ dissipative" energy; ensemble structural/ order/disorder; uncertainty with regards or in or of some thing; if diluted(?;extended), it can also include any distortion from something compared with a defined version of that thing; any deviation from the expected or even the desired; any unplanned/reasoning error. There may be more.

Our question is, if entropy is applicable to a set of axioms (may i call axioms as a set of 'primitive statements" derived/composed in an effort to abstract the characteristics of any one set of "observations"; so that all the observations may be derived from axioms/postulates, probably through the route of conjectures/hypothesis and theorems/theories/prepositions)--and the euclidian system we are considering should be taken to include only axioms and are also theorems, etc? I think i would first restrict myself to axioms. I have also to take up your expression

>

[i have used a REINTERPRETATION **appropriation** because i am more concrned with "use making" rather than "deriving" the approximation].

$$ unprimary use= necessary unusable energy as a biproduct of productive usable work.

1. Now, shall i consider the potency as the ability to derive theorems and applications? In that case,it is subject to entropy; concepts(somewhere becoming assumptions), can mislead thoughts, therefore? But do concepts themselves mislead--they can mislead an unassuming user who makes use of acquired knowledge/wisdom/concepts--so in that way, concept's/potency's use is subject to entropy.

2. I don't know if i would be right, but can axioms/concepts/theorems [i do no mind treating these as relatable] be treated as abstract nouns? Then if the euclidian system is an abstract noun type of entity/underlying content/truth,

i think these are not subject to entropy,since i think truth or primitives by definition has to be so.

[i had always felt abstraction after some depth starts resembling subjectivity almost; what is the proof of the most primitive words/statements; they are primitive only because we are almost certain not to find a reason or ability to further abstract].

ie truth begins where entropisibility stops. $

Now we have to start thinking, how in fact abstract nouns [potency/ use potency/ "before the intervention of external meaning and/or external requirement of purpose";

that is, restricted exactly to "meaning" the axiom/potency intends to represent and no more intentions; a truly closed meaning situation]

can be acted upon by entropy. I think the very of concept of a "true believable/usable axiom/primitive" will be rendered not-so if we allow entropy to act on. ie i can only say, if entropy acts on then it's not an axiom/primitive or such system. I have produced a tautology here. That means, either i have reached a truth or an assumption(axiom) OR i have reached my limitations.

$ overgeneralisation? i hope, ultimately, it's reconcilable at least as sufficiently-unparticular/-general.

3. Is not there, even, a possibility that axioms may some day get affected. [You know i have not learnt memory, therefore i tend to verify atleast common knowledge items before i write. So i landed in]:

(1) You yourself said .

(2) wikipedia/euclidean geometry:

If such "updations" a result of, IF, then WHAT entropy? Now, entropy is a rare generalisation we are "able to treat" in both physical and (nonphysical)="abstract potency" realms (eg uncertainty/disorder). But here we are seeing a cross over: "gravitational field" threatening and affecting euclidian axioms/system, or the applicability of the axioms. If we want the axiomatic system [independent of Euclid] to continue to represent what it had so far done, then we have to admit improvisations/updations in to it, 2500 years later; will this action be ultimately traced to the ineluctibility of entropy [physical systems or mathematical systems].

4. Is there some equivalent concept arrived at by mathematicians, independent of reference to entropy, from some thought world, some how unknowing to connect with "entropy" while thought making, but finally could wonder have landed on something resembling? This question because Bill may know such instances if.

nonphysical = i don't think physics and mathematics exceed from being equalizible to each other [not 2=2 type, but 2=b type] atleast outside of non-exixtence and ill-logic.

ill-logic = originally read in SPAN magazine (Pub: USIS, in India)in 1970s, , an article calling the logical errors caused due to affected thinking during illness. Here, i have used when i could have used illogic. I meant "ill"Logic?!

I made a google search for "mathematical equivalent of entropy" (without quotes). What a plethora of results. [but i could not localise/locate my what]. I think with human population what it is, no question is worth asking, our/my significance even if in a teleological-moment is only in picoprobabilities. But i must not abandon at least that!

The probable reasons my postings are long are because, that i have not learnt memory hence i need to workout every time; that i am being adventurous in attempting to write here. Hope i shall improve.

GS: "If Euclidean Geometry Doesn't exist, how come you are talking about it?"

It doesn't exist as an actuality, but it is a potency. There are many such things that mathematics deals with. Infinity, for example, does not --- so far as man can determine --- correspond to any physical actuality. But the universe is sometimes said to be potentially infinite.

Euclidean geometry is an important mathematical system. It approximates many things very well. Architects and engineers use it every day --- as I am sure you are aware.

GS: "I think you are being intentionally naive, or using an overly restricted definition of exist."

I don't think I said it doesn't exist. I said it is not actual, but potential.

I believe I have a broader concept of existence than the majority of the people who I find posting to this group. Most limit existence to substance. I recognize six 'categories' as well as transcendental being.

Euclidean geometry belongs to the category of quantity. Quantities exist in two ways, as quantifiers and as potencies. So far as I know there is no actuality precisely quantified by Euclidean geometry. But it approximates a great many things.

GS: "Air can't push a ball, in vacuum, but it can in Atmosphere, reference high winds, and hurricanes that put balls through windows etc."

In general Air doesn't push an projectile forward in the atmosphere, it holds it back. Or to be more exact, while the air at the back side of a projectile does push it forward, the air it meets going forward more than compensates for that.

Aristotle was simply wrong, as Newton pointed out. Force is required for acceleration or deceleration, but not for constant straight line motion. F=MA.

GS: "However I admit it is not the base case, and you do not get constant velocity in air because air is always associated with gravity (On the Surface of the Earth) and so you get a trajectory that curves according to the accelleration of gravity. I assume your Astronauts are at a lagrange point and therefore have a net null gravity effect?"

As I understand Einstein's General Relativity, gravity is not a force, but is the effect of the curvature of space.

In the example of an astronaut throwing something to another astronaut, as soon as the projectile is released it would continue on its own orbit around the earth. That orbit would differ slightly from that of the astronauts, so they would see its trajectory curving ever so slightly. Would they notice the variation from a straight line? It would seem that the difference between the projectile's relative velocity and the common orbital velocity would be insignificant, so I would doubt they would notice the difference. But who am I to say?

GS: "But whether or not there is a Force keeping it moving, the fact is that there is no reason to claim that inertia is wrong."

I never said that Newton was wrong. What I said was that he was right. F=MA.

SN: "If such "updations" a result of, IF, then WHAT entropy? Now, entropy is a rare generalisation we are "able to treat" in both physical and (nonphysical)="abstract potency" realms (eg uncertainty/disorder). But here we are seeing a cross over: "gravitational field" threatening and affecting euclidian axioms/system, or the applicability of the axioms. If we want the axiomatic system [independent of Euclid] to continue to represent what it had so far done, then we have to admit improvisations/updations in to it, 2500 years later; will this action be ultimately traced to the ineluctibility of entropy [physical systems or mathematical systems]."

The updating that has been done was to fill in 'logical holes' in Euclid's system. Euclid stated five 'postulates' and five 'common notions.' Unfortunately, some of the techniques he used to prove theorems were a bit sloppy. In order to clear up certain logical deficiencies in his system a number of additional assumptions had to be added to the original ten.

This updating has nothing to do with Einstein or with gravity. Euclid's original postulates and common notions are true in the updated systems... otherwise they wouldn't be Euclidean.

Tarski and Givant proved that elementary geometry is consistent, complete and decidable...

http://en.wikipedia.org/wiki/Tarski's_axioms

Ok, "As I understand Einsteins general relativity, gravity is not a force, but is a curvature of space.

While technically you are correct, the problem with that statement is that you are assuming that space curves without some force acting to perturb it.

Further, F=MA and anything with gravity has mass, and anything in a gravity field has accelleration so ipso facto there must be a force associated with gravity. Since this is true, it is important to realize that gravity is BOTH a curve in space, AND a force.

GS: "While technically you are correct, the problem with that statement is that you are assuming that space curves without some force acting to perturb it."

Well, we are getting close to the fringes of my understanding. I don't know that Einstein would use that term.

GS: "Further, F=MA and anything with gravity has mass, and anything in a gravity field has accelleration so ipso facto there must be a force associated with gravity. Since this is true, it is important to realize that gravity is BOTH a curve in space, AND a force."

Again, we are on the fringe of my understanding. From what I understand, Einstein would have it that an object in a gravitational field is simply following the shortest distance between two points in curved space... that it doesn't really accelerate relative to the curvature of space and time, but may seem to accelerate in a particular inertial frame.

But certainly there is a virtual force, if not a real one... matching the apparent acceleration.

Doggone it Bill, quit agreeing with me! I don't know how to take it!

#H1-181. Ref Bill Overcamp, Jan 6, 2011 12:24 am. *Updations*, ok.

But:

(2) wikipedia/euclidean geometry:

@*. Your treatment please for the *approximation..only where*.'

If Euclidean geometry will not work, then one uses some other geometry... hyperbolic, elliptical, or whatever. Not being a physicist, I would not know which to try.

I think that is the point Bill, even a physicist can't make the determination of what type of geometry to use, in a vacuum. There is the need to advance a new paradigm to explain why one geometry should be used over another, and since the system is naturally hostile to new paradigms, this is a difficult decision even for a well informed physical scientist.

Its how people perceive the things...

Or probably they are two ends of a linear scale? What will link both? A definition of Order? Number of steps or variables or sub-parts determining the state/structure? For example, how to perceive the simplicity/complexity of the limited continuum/continuibility of cells, organs and human body? Or more simply, the interplanetary dust or interplanetary space to the solar system.