Self organizing systems : Conway's The Game of Life

[Imparcticle]

http://www.math.com/students/wonders/life/life.html

After reading this article, I thought it would be a good research project to do for a science competition I'm planning on entering. Is it something worth spending a year researching on?

The thing that intrigues me is the possibility of applying it to our understanding of this question: "why is the universe disorderly". Am I correct to say that without disorder, there can be no "improvements" (by improvements, I mean in terms of human affairs)? Why is it impossible to have an orderly universe? Just what do we mean by "order"?

 

[loseyourname]

A perfectly ordered system would be in permanent equilibrium. With no possibility of chemical reactions, there is no possibility of life.

 

[Imparcticle]

how do we know that order must mean there is equilibrium?

How do we know that equilibrium isn't disorder? Obviously, the universe, which is in constant entropy "balances itself out" very well.

 

[Janitor]

I remember reading in the 1970s or early 1980s that there was a newsletter devoted to Life. I never saw the newsletter, but it sounded pretty neat. Two-dimensional automata have been thoroughly investigated by Wolfram, but you might want to look into what sort of three-dimensional automata rules give the possibility for interesting evolution from an initial state. I guess the drawback to 3D is the problem of visualizing a state on a flat computer screen or piece of paper. If you wanted to look at the state of a 10x10x10 cluster of cube-shaped cells, you would have to visually examine a set of 10 squares, each one being a 10x10 slice of the cluster.

 

[BobG]

SUN used this game as what I feel is the best screen saver, ever. It started with an oscillator (usually more complex than just a 2 period oscillator). Then a glider enters and works its way towards the oscillator. When the glider ran into the oscillator, all hell would break lose with all kinds of new patterns emerging. Looked kind of like a virus attacking a living cell.

This also provided a pretty entertaining moment for our satellite simulation shop. Our simulator had two Sun computer stations, one monitoring the simulation (all the satellite telemetry points, etc) and one for support. Since the support station didn't have to be used much after the simulation was set up, it usually went into screen saver mode. We had a general visit our squadron and he took a tour of all of our facilities, including seeing how we ran satellite simulations for training the satellite operators (I was one of the instructors). Our young briefer sets the general down in front of the operating simulation station, but naturally the screen saver is what catches the general's eye. He turns his chair around and watches the screen saver throughout while the poor, frustrated briefer diligently explains how the simulator works and all the key points on the operating simulation station. I nearly died laughing (afterwards, of course) - I just wonder if anything the briefer said seemed to have any relevance to what the general was watching on the screen and what his impression of our simulator was?

 

[loseyourname]

how do we know that order must mean there is equilibrium?

How do we know that equilibrium isn't disorder?

Because that is the way we define the words. They don't mean anything other than what we say they mean.

 

[wuliheron]

http://www.math.com/students/wonders/life/life.html

After reading this article, I thought it would be a good research project to do for a science competition I'm planning on entering. Is it something worth spending a year researching on?

The thing that intrigues me is the possibility of applying it to our understanding of this question: "why is the universe disorderly". Am I correct to say that without disorder, there can be no "improvements" (by improvements, I mean in terms of human affairs)? Why is it impossible to have an orderly universe? Just what do we mean by "order"?

Your question is not a scientific question, but a metaphysical philosophical question. Science is not in the business of making absolute pronouncements about the nature of life, the universe, and everything.

Note that your assumption can easily be turned on it's head and make just as much sense, "Without order, there can be no improvements." Without a specific context, the words are meaningless, and you can cut and paste any words you want. For example, "Without energy, there could be no improvements," or "Without change there could no improvements."

You have already indicated what "order" means, words only have demonstrable meaning according to their function in a given context. In this case, you supplied the most basic context which no one can avoid, the context of being human. Order and chaos only have meaning because we give them meaning, and that process is evidently relativistic.

For me, up is the equivalent of down for a china man on the opposite side of the earth. Sipping on my cup of coffee, it looks remarkably orderly to me. To someone studying thermodymics and the motion of subatomic particles, it is a complete cacophany of chaos.

 

[Imparcticle]

So my questions are meaningless?

 

[wuliheron]

So my questions are meaningless?

It just depends upon the context. Any question can be meaningless when taken out of context.

 

[Imparcticle]

Well, the universe is perfectly balanced, is it not? (please answer "yes" or "no")

 

[sol2]

Srinivasa Ramanujan

You might like http://large.stanford.edu/rbl/lectures/index.htm

How would such numbered systems arise if we had not realize a immediate consequence to quantum geometry that would have defined any method arising out of some math structure.

Consider the marble drop as a probability, and from it, an emergent system?

Discovering patterns


So how would we find understanding with http://superstringtheory.com/forum/metaboard/messages18/186.html

A neurual synapse that allows a extraordinary amount of information to enter yet it is based on harmonical laws?

 

[yesicanread]

Disorder.

Disorder.

If 1 triangle is seen, it has a tripod effect. In seeing the triangle, you see three points, and define a plane.

If I understand Einstein, who agreed with Newton, and is referenced in plank physics. Gravity is shaped like this - U. In effect, Gravity considers the plane, and therefore the triangle.

Disorder isn't in the plane/gravity. It's in seeing the plane. There is infinite variation there in considering the human, creatures great and small shifting about, in seeing various planes. In effect What sees the plane creates disorder, right ?

Time travel is a person saw a plane/experienced gravity, then doesn't see the plane. If seeing is perception, we percieve with our senses, perception = perception.How old are we people anyway. We travel back to a perception made previously and percieve it again. Time travel.

Disorder.

 

[sol2]

http://www.walterzeichner.com/thezfiles/time2.gif

http://wc0.worldcrossing.com/WebX?14@107.YQwEcFOdowZ.1@.1ddea281/0

 

[loseyourname]

Well, the universe is perfectly balanced, is it not? (please answer "yes" or "no")

How can one answer a question this vague? What do you mean by perfectly balanced? It is not sitting on one end of a see-saw with a second universe of equal weight sitting on the other end. I can tell you that.

 

[wuliheron]

The Fish! The Fish!

 

[Imparcticle]

Disorder isn't in the plane/gravity. It's in seeing the plane. There is infinite variation there in considering the human, creatures great and small shifting about, in seeing various planes. In effect What sees the plane creates disorder, right ?

How is disorder in something?

In effect What sees the plane creates disorder, right ?

In saying this, it seems to me you are implying that disorder is dependent on an observer.
Time is the increase in disorder in the universe. If, as you say, seeing is what creates disorder, then time is created by seeing...but seeing is an action which takes time. So time must exist in order for you to see anything.
I think the answer to your question is "no".

How can one answer a question this vague? What do you mean by perfectly balanced? It is not sitting on one end of a see-saw with a second universe of equal weight sitting on the other end. I can tell you that.

Allow me to illustrate then. If the weak force was slightly weaker, then there would be too much atomic decay. If the ratio between the strong force and EM force was slightly (that is, a minute scale) altered, then there wouldn't be as many chemical reactions (which are neccesary, as you know, for the sustainance of life and its creation). If electrons were slightly bigger, they'd combine more often, and create neutrons and this would mean hydrogen wouldn't exist as well as disrupting other chemicals. If the strength of the gravitational pull on a star was slighlt increased, the rate of nuclear reactions in the star would increase; if it was decreased, matter would not be as we know it, that is, there wouldn't be stars or galaxies.

I think the universe, in the aforementioned sense is balanced perfectly (from a human perspective).

 

[loseyourname]

So you're saying all force and mass constants are such that there exists the possibility of complex systems, including organic life. That didn't seem to be your original point, though. Your original point was about the necessity of disequilibrium, and the ensuing entropy-driven reactions, to the arising of complexity and life.

As to your initial questions:

"Why is the universe disorderly?" (Again, I'm going to assume that you mean to ask why the universe is in a state of disequilibrium.)

The answer is simply that some initial event (big bang, God made it that way, what have you) put the universe into disequilibrium, and the initial free energy was such that there is still a huge surplus today.

"Am I correct to say that without disorder, there can be no 'improvements?'"

Again, presumably by improvements you mean [entropy-driven reactions (that is, catabolic reactions) whose energy can be harnessed to drive anabolic reactions and thus build up complex systems, including life]. Yes, disequilibrium is necessary for this to be possible.

"Why is it impossible to have an orderly universe?"

I suppose I can annoyingly answer this question with another question: What makes you think an orderly universe is impossible? While it may be true that quantum fluctuations make it impossible to have perfect equilibrium on a subatomic level, the loss of net free energy in the universe, combined with the eventual decay of the proton, should eventually lead to a universe in which no chemical reactions take place, and so chemical equilibrium (substitute in "order") will be achieved.

"Just what do we mean by 'order?'"

It should be obvious by now that I mean chemical equilibrium.

 

[yesicanread]

Q: How is disorder in something ?
A: A plane is a part of geometry.
Geometry is called intersection also.

A perpendicular vertex line segment to a plane is a variable. This is a intersection. This is geometry.

Geometry is in a plane, and inseperable from a plane. Disorder created by a variable vertex altitude is the perpendicular line, that when the action is created by the vertex to the plane, has a equal and opposite vertex to descend too. This variable is constantly changing.

No time does not affect the vertex altitude, not in my geometry lessons.

We see with two eyes, mostly. They make a point of seeing. This is a type of vertex perpendicular line segment that makes a point out of seeing geometry, including planes. ~ .

Seeing, thus perception, does create disorder. Time is created by the vertex perpendicular line segment variable, thus seeing does create time. And how can there be infinity if there is action to create a equal and opposite reaction ? Huh.

 

[Imparcticle]

So you're saying all force and mass constants are such that there exists the possibility of complex systems, including organic life. That didn't seem to be your original point, though. Your original point was about the necessity of disequilibrium, and the ensuing entropy-driven reactions, to the arising of complexity and life.

What I said on my previous post is also part of my point. I will arrive at my actual point step by step (I find it helps people understand my ideas better). First, I'd like to go over the idea of a disorderly universe:
Apparently, (according to my previous post) there is a certain level of order in the universe, right? As I said, if certain forces were either decreased or increased, it would dramatically change the way the universe works. There is a basic order in this, is there not?

As to your initial questions:

"Why is the universe disorderly?" (Again, I'm going to assume that you mean to ask why the universe is in a state of disequilibrium.)

The answer is simply that some initial event (big bang, God made it that way, what have you) put the universe into disequilibrium, and the initial free energy was such that there is still a huge surplus today.

Something put the universe into a state of disequilibrium? What kind of state was the universe in before?

"Why is it impossible to have an orderly universe?"

I suppose I can annoyingly answer this question with another question: What makes you think an orderly universe is impossible? While it may be true that quantum fluctuations make it impossible to have perfect equilibrium on a subatomic level, the loss of net free energy in the universe, combined with the eventual decay of the proton, should eventually lead to a universe in which no chemical reactions take place, and so chemical equilibrium (substitute in "order") will be achieved.

What's net free energy?

"Just what do we mean by 'order?'"


It should be obvious by now that I mean chemical equilibrium.

I concur.

Loseyourname: Do you understand yesicanread's usage of "disorder"?? if so, please explain it to me, if it is convenient.
Also, have you read my reply in the thread "quantum cells" in the biology forums? I am interested in your opnion of it.

 

[sol2]

What is entrophy?

Can boundaries when decreasing, create disorder(collapse of black hole)?

If energy is confined what happens? What does the marble drop represent?

http://physicalworld.org/restless_universe/figs/fig_1_15lrg.jpg

Ludwig Boltzmann
(1844-1906)

In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease
http://physicalworld.org/restless_universe/html/ru_bolt.html

Entropy and the second law of thermodynamics provide the key to understanding equilibrium. An isolated system, free from all other influences, may undergo various spontaneous changes, some of which will increase its entropy. If the total entropy increases during a process, as it usually does, the process is irreversible - it is impossible to return to the starting point, leaving no other traces, since that would require a decrease in the total entropy, which is impossible. Once the entropy has increased, it cannot decrease again. An isolated system therefore approaches a state in which the entropy has the highest possible value. This is a state of equilibrium. In equilibrium, the entropy of the system cannot increase (because it is already at a maximum) and it cannot decrease (because that would violate the second law of thermodynamics). The only changes allowed are those in which the entropy remains constant.

http://physicalworld.org/restless_universe/html/ru_3_21.html

http://apollo.lsc.vsc.edu/classes/met130/notes/chapter2/sb_law.html

To move from euclidean perspective to non euclidean perspective, holes become a interesting perspective?

In curved space the rules of Euclidean geometry are changed. Parallel lines can meet, and the sum of the angles in a triangle can be more, or less than 180 degrees, depending on how space is curved. Einstein's theory gave a correct prediction for the perihelion shift of Mercury. It also explained why objects fall independent of their mass: they all follow the same straightest possible line in curved space-time. Finally, in Einstein's theory the instantaneous gravitational force is replaced by the curvature of spacetime. Moving a mass causes ripples to form in this curvature, and these ripples travel with the same speed as light. Thus, a distant mass would not feel any instantaneous change in the gravitational force, and special relativity is not violated.
http://theory.uwinnipeg.ca/mod_tech/node60.html

So if we consider the "energy" of the system, how dynamical could this system become?

So you know that standard flat space is has a metric equivalent O but energy remains in the system, so how could this be(Quantum Harmonic oscillator)? To a much more complex scenario, supergravity would have to consider supermetric points.( this would have been able to describe a very fluid universe that if topologically considered, is very smooth)

So how would you effect isolated systems like a Blackhole? Its in the way you can transfer information inside? If you do not understand this, then you would not understand sonoluminence.

 

[yesicanread]

Very fascinating in a marveling way, Sol2. Your last post here I mean.

I just marvelled though. Didn't bother reading it. :shy:

 

[yesicanread]

Metric/supermetric points, is very smooth.

Did I understand that point properly ?

Then you said something about transfering info inside.

I've described this scenario above in my geometry post in this thread. :surprise:

 

[selfAdjoint]

"Just what do we mean by 'order?'"

It should be obvious by now that I mean chemical equilibrium.

Equilibrium is a state of maximum disorder (maximum entropy, minimum free energy).

 

[wuliheron]

Ya'll seem so busy applying a reductionist approach to the subject, that you've forgotten it is a holistic theory.

For a more insightful look at the concept, I recommend the work of Jim Rough. He is a physicist who worked in this field, but then went on to translate the results into other fields of endevour. Here is one of his websites:

http://www.tobe.net/

 

[gravenewworld]

Is there really order in the universe? The only reason that the molecules in your body exist in great order is beacuse the entropy, or disorder, or the universe increases. The amount of entropy that increases in the universe must be greater than the amount by which entropy decreased to make up well ordered molecules of your body. Entropy in the universe is always increasing. The BIG question is whether or not there is a maximum amount of entropy in the universe. What will happen when entropy reaches a maximum? No chemical reactions will be possible, no ordering molecules into larger structures will be possible.

 

[yesicanread]

Loseyourname: Do you understand yesicanread's usage of "disorder"?? if so, please explain it to me, if it is convenient.

I just pasted this from my theory development.

Quote:
1.) I began looking at the plane as if the vertex had two points on the plane.
I considered that if I used simplexes the conversion from three points to two could be made.
That way I use a plane and initiate a plane using two or three points.

Reason: Which is possible since three points define a plane and the scenario would allow be use of geometry or conversion.

If the simplexes are joined be a altitude between vertexes and the points on the plane equal each other. It may in fact resemble a sphere. Also If I convert back to using just two points on the plane. The degrees used in both triangles equal 360 degree. A circular type shape, a circumference.

Since I don't know which two points I use. The 360 degrees may use different points on the plane. So all sides of the simplex may be seen as circular. And thus the entire simplex has circular sides that meet equal points on the plane. A sphere.

So the simplex or two point vertex has a circular/spherical equivilenence, and may be call AB.

2.) Alright. I'll let the Equivalence Principle go. So I'll use this. What if when two points on the plane are used, point symmetry was made. Then, the vertex started the action. Newton's equal and opposite reaction says this action has a equal and opposite reaction. As well as the reaction caused by reaching the plane. Acceptable with black hoples when they bust. Their pull is a push. Newton.

If altitude has a action. It can't be infinite hight. But the variation on the plane is inmeasureable one would suppose. Edit:(This is disorder I think.)

3.) Because action reconverts to action. The reaction is equal and opposite the action. And so when we create a circular/spherical/planar/geometric movement. That action has been converted back to action/reaction. and passed through reaction to convert to reaction.

And so my description is complete intersection/geometry. Points/vertexes, Planes, and lines/altitudes from vertexes. And a description of Newton, however general, Which guided Einstein, and guides today's physicists.

Get that? I haven't broken any rules I don't think.

I've tried to be basic. It helps these type of concept/perception become understood in basic general knowledge. That is my goal, as I don't like fancy dancy theories.
End quote.

Feedback would be special to me.

 

[Imparcticle]

sol2:
Can boundaries when decreasing, create disorder(collapse of black hole)?

If energy is confined what happens?

If your first question was rhetorical, then I think you answered your second question. If my assumption is incorrect, am I right to assume, on the other hand, that both questions are regard the same basic idea?
Can disorder be created?

From dictionary.com:


cre·ate ( P ) Pronunciation Key (kr-t)
tr.v. cre·at·ed, cre·at·ing, cre·ates
1.)To cause to exist; bring into being. See Synonyms at found1.
2.)To give rise to; produce: That remark created a stir.


In which context (1 or 2) do you use the word "create" in?

sol2:
Ludwig Boltzmann
(1844-1906)

Quote:
In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease
http://physicalworld.org/restless_u...ml/ru_bolt.html






Quote:
Entropy and the second law of thermodynamics provide the key to understanding equilibrium. An isolated system, free from all other influences, may undergo various spontaneous changes, some of which will increase its entropy. If the total entropy increases during a process, as it usually does, the process is irreversible - it is impossible to return to the starting point, leaving no other traces, since that would require a decrease in the total entropy, which is impossible. Once the entropy has increased, it cannot decrease again. An isolated system therefore approaches a state in which the entropy has the highest possible value. This is a state of equilibrium. In equilibrium, the entropy of the system cannot increase (because it is already at a maximum) and it cannot decrease (because that would violate the second law of thermodynamics). The only changes allowed are those in which the entropy remains constant.

http://physicalworld.org/restless_u...ml/ru_3_21.html

Is this not a description of an organized universe?

sol2:
So how would you effect isolated systems like a Blackhole? Its in the way you can transfer information inside? If you do not understand this, then you would not understand sonoluminence.

Please enlighten me (or us) about this sonoluminence. How is a black hole an isolated system? Is it becaus it pulls on everything it's gravity can reach (if there is a techinical name for this, please tell me)? Thanks.

selfadjoint
Equilibrium is a state of maximum disorder (maximum entropy, minimum free energy).

This is where I have difficulty. Consider this:

From dictionary.com, the first and third definitions for "equilibrium"


e·qui·lib·ri·um ( P ) Pronunciation Key (kw-lbr-m, kw-)
n. pl. e·qui·lib·ri·ums or e·qui·lib·ri·a (-r-)
A condition in which all acting influences are canceled by others, resulting in a stable, balanced, or unchanging system.

Physics. The state of a body or physical system at rest or in unaccelerated motion in which the resultant of all forces acting on it is zero and the sum of all torques about any axis is zero.

So by definition, equilibrium is an unchanging, balanced system.

from dictinary.com, the definition for disorder:


dis·or·der ( P ) Pronunciation Key (ds-ôrdr)
n.
A lack of order or regular arrangement; confusion.


Disorder, on the contrary is a state of irregularity.

How then, can maximum disorder lead to an opposite state, that of order (or equilibrium)??
My question may be meaningless when I think about it. Here's why:
If you recall my post which, in summary, pointed out the balanced states of certain forces. How do we know the forces are really balanced? How do we know they aren't? Just because the universe would change dramatically if slight changes occurred does not mean there is balance. It just means the universe would be different. Of course, "balance" means "a state of equilibrium". The universe is not in a state of equilibrium.

I wonder, is there an inverse relationship between disorder and order? Could they be interdependent?? There must be a relationship..somewhere!

Earlier, I thought of the possibility that disorder=order. .
Now I am thinking otherwise. I really am confused. This is why I need help with this, desperately.

 

[Imparcticle]

yesicanread
1.) I began looking at the plane as if the vertex had two points on the plane.
I considered that if I used simplexes the conversion from three points to two could be made.
That way I use a plane and initiate a plane using two or three points.

What's a simplex? I should probably point out I'm just in 9th grade and studying Euclidean geometry. So if this is higher math, I may be a little slow in understanding.

But I am still interested in understanding your idea as much as possible.

 

[Imparcticle]

"Am I correct to say that without disorder, there can be no 'improvements?'"

Again, presumably by improvements you mean [entropy-driven reactions (that is, catabolic reactions) whose energy can be harnessed to drive anabolic reactions and thus build up complex systems, including life]. Yes, disequilibrium is necessary for this to be possible.

Ah, speaking of imporvements...
I was thinking about the subject when we were at the gas station. Gas prices are soaring, so people get stressed out; they may have to squeeze their budget for gas. When in trouble, some people may look for alternatives. Part gas and electric cars become more popular ideas. In fact, such cars have just come on retail. Recently, I was reading a SCIAM article about alternatives for gas: fuel cells. Such alternatives only have a greater chance of becoming a reality when they are needed. Therefore, the uncertainty and confusion over gas prices [disorder] eventually lead to an alternative [which then has its own problems, eventually that is] and so on.

Have I observed a logical relationship?

 

[yesicanread]

Simplex.

Simplex: A three simplex is a triangular base with pyramidal sides meeting at a point at the top.

According to Mr Kaku/Selfadjoint I think.

 

[yesicanread]

This one's easier for me.

1.) I began looking at the plane as if two opposite vertex's had two equal joining points on a plane axis. I considered that if I converted the two points used on the plane I could make a simplex, the axis/plane has three planar points right, and since the plane has three points I could make three sides to the simplex.

Reason: Which is possible since three points define a plane and the scenario would allow be use of geometry or conversion.

If the simplex vertex's are joined on the plane and by a perpendicular altitude between them. It may in fact resemble a sphere. Also If I convert back to using just two points on the axis plane and the vertex's. The degrees used in both triangles equal 360 degree. A circular type shape, a circumference. This 360 degrees may use different points from the plane, and still equal 360 degrees. So all sides of the simplex may be seen as circular. And thus the entire simplex has circular sides that meet equal points on the plane, and are equal. A sphere.

So the simplex or two point vertex has a circular/spherical equivilenence, and may be call AB.

2.) What if when two points on the plane are used I made point symmetry, and the one vertex starts the perpendicular action to the opposite equal vertex. Newton's equal and opposite reaction says this action has a equal and opposite reaction, the plane, as well as the reaction caused by reaching the opposite vertex.

If altitude is action from the vertex, it can't be infinite hight.
But the variation on the plane is inmeasureable one would suppose.(This is disorder I think.)

3.) Because action reconverts to action. The reaction is equal and opposite the action. And so when we create a circular/spherical/planar/geometric movement. That action has been converted back to action/reaction. and passed through reaction to convert to reaction.

4.) And so my description is complete intersection/geometry.Points, Planes, and lines.
and a description of Newton, however general, Which guided Einstein, and guides today's physicists.

 

[Imparcticle]

1.) I began looking at the plane as if two opposite vertex's had two equal joining points on a plane axis. I considered that if I converted the two points used on the plane I could make a simplex,

Convert in what manner?

the axis/plane has three planar points right, and since the plane has three points I could make three sides to the simplex.

What is a planar point?

If the simplex vertex's are joined on the plane and by a perpendicular altitude between them. It may in fact resemble a sphere. Also If I convert back to using just two points on the axis plane and the vertex's. The degrees used in both triangles equal 360 degree. A circular type shape, a circumference. This 360 degrees may use different points from the plane, and still equal 360 degrees. So all sides of the simplex may be seen as circular. And thus the entire simplex has circular sides that meet equal points on the plane, and are equal. A sphere.

So the simplex or two point vertex has a circular/spherical equivilenence, and may be call AB.

That is brilliant. Did you contrive this yourself?

What if when two points on the plane are used I made point symmetry, and the one vertex starts the perpendicular action to the opposite equal vertex. Newton's equal and opposite reaction says this action has a equal and opposite reaction, the plane, as well as the reaction caused by reaching the opposite vertex.

If altitude is action from the vertex, it can't be infinite hight.
But the variation on the plane is inmeasureable one would suppose.(This is disorder I think.)

Consider a line which is constituted by an infinite set of points. Is there a line that is equal to this line? No. It is meaningless to prescribe a property of equivalency to an infinity. Is there an opposite line? The opposite of infinity, I presume (I could be incorrect) would be an absence of it, which, considering Zeno's Paradoxes would indicate an absolute nothingness...which doesn't make sense either (if you'd like me to explain why, I'd be honored, as it is my favorite subject to explain).

Anyway, my point here is regarding your application of Newton's 3rd Law of Motion to Euclidean geometry. How about Hyperbolic or Reinmann geometry?

 

[yesicanread]

Convert in what manner?
Answer. The vertex had a single point. The two planar points on the plane + the vertex are 3 points. Three planar points define a plane.



What is a planar point? Three non-collinear planar(on a plane) points define a plane.



That is brilliant. Did you contrive this yourself?
Yes.

Consider a line which is constituted by an infinite set of points. Is there a line that is equal to this line? No. It is meaningless to prescribe a property of equivalency to an infinity. Is there an opposite line? The opposite of infinity, I presume (I could be incorrect) would be an absence of it, which, considering Zeno's Paradoxes would indicate an absolute nothingness...which doesn't make sense either (if you'd like me to explain why, I'd be honored, as it is my favorite subject to explain).

Anyway, my point here is regarding your application of Newton's 3rd Law of Motion to Euclidean geometry. How about Hyperbolic or Reinmann geometry?

I describe geometry. It follows.

- Vertex, from which I draw a altitude joining two vertices. Is one point.

- Plane. Which is three sets of two points: Triangle inequality theorem.

Which each constitute 360 degrees(A circumference) when used with the opposite perpendicular vertex's bisected by the plane.

- Line. The altitude(Note. I saide altitude/hight)between each vertex is perpendicular.

- These three things constitute geometry. Geometry is termed Intersection as well.

I then stated the idea of the vertex having two properties. 1.) A vertex. 2.) 3 bisected circumferences, joined on a bisecting plane with a equal and opposite setup.

The plane is three sets of two points: triangle inequality theorem. It is not circular. So the property is AA, or BB.

Then. Newton's third law says the vertex causes a equal and opposite reaction/Vertex acting on the plane. Also the opposite vertex equals it, so both the plane and opposite vertex experience action from the vertex.

I didn't break the definition of Geometry or Newton. I unified them. And the science that uses them, basically all science.

Peace.

b11ng00

 

[ryokan]

http://www.math.com/students/wonders/life/life.html

After reading this article,

I suggest the reading of other old papers on cellular automatons.
For example, Physica 10D (1984) 1 - 328.
It can be also interesting Cellular automata machines (Toffolli and Margolis) MIT Press. 1987.
It seems to me also interesting the recent work of Wolframm: A new Kind of Science in www.wolframscience.com

 

[Imparcticle]

I didn't break the definition of Geometry or Newton. I unified them. And the science that uses them, basically all science.

So you're saying that there is something that is equal and opposite to a line? (i.e., a line that is an infinite set of points)

I suggest the reading of other old papers on cellular automatons.
For example, Physica 10D (1984) 1 - 328.
It can be also interesting Cellular automata machines (Toffolli and Margolis) MIT Press. 1987.
It seems to me also interesting the recent work of Wolframm: A new Kind of Science in www.wolframscience.com

Wow! That's fantastic. I was afraid I'd have to buy the book! Thanks.

Do you think its possible for us to contrive a "logical" (i.e., "logical" in the sense that all our conclusions/theorems are based on axioms that we just made up, and don't neccesarily comply with the logic of this universe) system like that of cellular automata? In multiverse theory, it is said that there may be subuniverses that have physical laws that are in contradiction with ours.
BTW, in response to my own post on page two concerning disorder and order, I was wondering if it may be that what we see as order and balance are really not order and balance, but a state of fixed chaos.

 

[yesicanread]

So you're saying that there is something that is equal and opposite to a line? (i.e., a line that is an infinite set of points)

Um. I'm saying I didn't leave geometry undefined, and as well I didn't leave Newton's third law undefined.

As a matter of fact. You can translate the vertex, to the plane, to the vertex, and within this context, of possible translation. I have defined Geometry + Newton's third law = Unified stuff.

I said "Plane", and a bunch of other stuff. You should read what I typed out. Patiently, concidering every word. Kind of like right now.
:shy:

 

[ryokan]

I was wondering if it may be that what we see as order and balance are really not order and balance, but a state of fixed chaos.

As selfAdjoint wrote in his post, "equilibrium is a state of maximum disorder (maximum entropy, minimum free energy)". I think that other dictionary concepts of equilibrium are not applicable to the question that I suppose you pose here.
Equilibrium is a thermodinamyc concept. Change, evolution only have sense in a thermodynamic context: in the time's arrow.
The thermodynamics of irreversible processes (Ilya Prigogine...) is interesting as an explanation of how "order" can arise without contradiction with the second law. Such is the case of stationary status far from the equilibrium, which would be the case of biological systems.
I think that cellular automatons can be useful tools to simulation or to play. I don't have yet read the book of Wolfram. After its reading, it is possible that I think differently.