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Popcorn Sutton, But interestingly enough, the given is not possible. You cannot have an exactly precisely the same moment, again. Each moment happens only once. And if reproduction of the exact moment, were to be repeated, it makes sense to imagine that all those variables lining up the same way, would result in the thing that happened, because it did. But I will not give Mr. Dennett his given. That particular collection of stuff is no longer in play. Like the Earth making a cycle around the Sun, when it completes a year, things are not the same as they were a year ago. Rock has eroded, trees have grown, the Sun itself has continued on its course around the center of the galaxy, all the planets are in different relative positions, the Sun is in a different stage of its 14 or 11 year cycle or whatever it is. A moment is not repeatable, but in retrospect and imagination. You, as an engineer, know that chaos is a factor. Water slides are designed to keep the rider in the chute, but just a slight change in the flow of water at the top, can set up an oscilation that builds as it makes its way down the course, and every once in a while a rider is launched out of the course. And no two snowflakes are precisely the same. The exact conditions of pressure and heat and movement and humidity, gravity and particle attraction during the growth of the crystal, evidently disallow the creation of an oracle, a seed crystal, that HAS TO, grow to a particular exact shape. The universe is not determined. It has not yet done, what it is going to do next. Regards, TAR2

Mike, Conflating the whole image, is the pure size of everything, and as well the speed and complexity at which things of smaller than human scale, unfold. I am of the opinion that we absolutely have choice. It is ours to maintain that which we wish to maintain, destroy that which we wish to destroy and create that which we wish to create. That our reach is so limited, confuses people into thinking that that means our choices do not matter, when they absolutely matter...to us. Flashback to you (if you were an 11 year old boy, like I was once) and an encounter with an anthill. Did you not have the choice to excercise some control over those ants? Many of us 11 year old boys realized our power over that colony. Perhaps we wiped the hill away, to watch it rebuild, or took sides as we discerned an ant war occurring between the red ants and the black ants. Perhaps we squished a few, or fed the colony crumbs. Immaterial really, whether we excercised constraint and care, or wanton destruction. The point being, we had a choice, and the result of our choice mattered, at least to the ants. Does it matter, in the history of the world, probably not. Does it matter to a spinyark on a planet circling Alpha Centuri? Probably not. Did it matter to you and the ants? Absolutely. One other consideration, modifying a bit my statement suggesting that the twin towers are gone from reality. Since the speed of light is finite, there is no way the Spinyark could know what has happened here on Earth, over the last 4.4 years. A Quadrunk on a planet 15 lys from here has not experienced the fall of the twin towers. There might be an argument that the twin towers stand, in reality, in the area of the universe between the large spherical shell marked by the distance light could travel since they were built, and the spherical shell marked by the distance light could travel since they fell. In that mode of considering "everything" we would fall rather short in conceptual horsepower. We would not have a proper grasp, until we considered everything, from every possible "current" location, and that would just give us a grasp of one tiny slice of time, about as wide as our defined moment. Then there would still be the vast amount of earlier moments, and the likely vast amount of future moments to consider, before we could get anywhere close to feeling that we have considered "everything". In light of all this, I "choose" to consider that the universe has not done what it is going to do next. And being 100% universe material myself, I have something to do with what that next thing is going to be. Regards, TAR2

Mike Smith Cosmos, What seems un-multiuniverse to me, is that what ever you do, stays in this one, affects this one, and is done with the environment and the conditions, that this universe presents. Let's say for instance, that I choose to break a glass. That glass has lost its ability to hold water, and if I shattered it well enough, there is not anybody that will ever drink from that glass. I have choosen a path for this universe to take, that no longer includes that glass. And the pieces remain in this universe to be ground to sand or to cut people's fingers, that try to pick it up. Somebody decides to take down the twin towers, they remove the buildings from this universe, for everybody and everything in the universe. They have modified THIS universe, not created another one. There is NO universe that contains a Milky Way, with a Sun, with an Earth and a U.S. and a New York, with a lower Manhattan that has twin towers, anymore. Regards, TAR2

Split, I see your point about the vests. But that might be another thread, to discuss whether it was the vest, or the fact the shooter did not know you were wearing one, that saved your life. Like you said, if he knew you were likely to be wearing such a vest, he would have shot you in the head, or poisoned you, or burned you, or cut off your head with a sword. But to bring the vest idea, back to the thread, in terms of one person thinking they know what would "save" another...there is always, or nearly always, another way to look at a thing. A thing might "work" in many ways, and not work in other ways. Like the current style vest, that is not used for its intended purpose, because of the weight and heat...there are places were ANY belief, has some weaknesses or places they do not work, or places were a belief is "out of place". Let's say for instance one is very soundly ensconced in a university and is a leader of thought and integrity and knows many things, and believes many things and finds herself a survivor of a shipwreck on a desert island. Very few of her beliefs would apply to the situation, and stripped of her support system and technology, she may have to revert to lessons she learned in girlscouts, to survive. Knowing the square root of 3 or how to derive a fact from a logical proof, or knowing the best practices in business or politics might not be useful or pertinent. With no one else but herself and the island to depend on, her belief in the proper color of shoes to wear will not apply to the situation. She would not be bound by the laws of man, nor privy to the protection of her society. She would be on her own, to develop a workable relationship with the island...or die...unless she was rescued ("saved"). Regards, TAR2

Split, I will have to agree with you, when you put it that way, that people that believe in God are broken. At least those that fit the fanatic description. They have obviously mistaken the situation, and bought a line of crap, that has no bearing on, or function in, reality. They are, as you put it, either stupid pawns in the brainwashed and decieved young case, or insane in the sociopathic "leader" case. I forget who said it long ago in this thread, but to paraphrase that somebody "you can believe any damn fool thing you want, just don't make it affect me." Perhaps, as you shook in anger, retelling the story, beyond the anger you felt at yourself for not listening to your own instincts, was your anger at the insanity that the shooter had brought into "our" reality. In anycase Split, thank you, for what you do. I know you do it, on "our" behalf. Regards, TAR2

Split Infinity, I understand your point, about religious people that are operating with such a diverse mindset from "reason", that they cannot be reasoned with. One of my main reasons for trying to understand what people "mean" by god, was 9/11, where the action, done presumably in the name of Allah, to deal a blow to Satan, looked like nothing more than pure Evil to me. Death and destruction for no purpose, no goal, no sensible reason. I am an enemy of those that would be behind such a day as 9/11. I am not the enemy of the creator of the universe. Therefore the action was not taken by the creator of the universe, and anyone thinking that the creator of the universe was served by such an action, is in serious error. So for me, in this discussion, where belief in the creator of the universe is being equated with error and brokeness, I fully agree, as in the case of 9/11, where it is so obvious that the creator of the universe would not do such a contrary thing, and therefore it must be the act of broken persons, in serious error. This however does not convict God of the act, nor prove to us, that there is not a higher standard we should hold ourselves to. So if God exists, he wouldn't do that, and if God doesn't exist, he didn't do that by virtue of the fact that he doesn't exist to do that. Which leaves only us, to figure out what should and shouldn't be done, what standards to enforce and uphold, and what things are good and what things are bad for us, here and now, and for our children, who will take our places when we die. In this, the "idea" of God, of an overarching ideal that we are responsible to, and "working for", when we do our job correctly, is not a bad thing to believe in. However, if you think personally, that you are the only one on the job, the only one doing it right...you have somehow missed the point. Regards, TAR2

Moontanman, I know we have discussed the extension of the social animal idea through to super Alpha males (presidents and kings) and laws can be thought of as pack rules, written down and improved on and tested against all conflicts as they arise, and you COULD imagine us getting to something like we have, without the idea of God...but that is not the way it went down. We HAVE this idea of God...enough at least for people who don't "believe" in God, to know enough about the idea, to consider it "untrue", or to consider God dead, or to consider the idea of no further use to us. Its this fact that our history has this idea in it, that has me considering that we would not be exactly here, without it. And even people who don't need the idea, or have rejected the idea, or those who KNOW the idea is only an idea and not a real entity, still use the term, and describe what characteristics of a particular named God, are obviously impossible or unworkable. And of course there is the fact that billions of humans consider whatever image they have of God to be an image of a real existing consideration. And these billions make up a goodly portion of our civilization and are that proportion of the humans that make and follow and uphold the laws we live by. In the context of the thread one would have to consider half the world broken by virtue of their belief in God. And of these many thusly "broken" folk, there must be a large percentage, that are actualy holding the place together. And at least in this, one could argue, that it does not actually "hurt" to belief in God. Split Infinity, Except in your types, who will kill in the name of their God. But then again there are people that will kill in the name of their country, or their leader, or their philosophy, or kill for a buck, or for power and control, or to simply protect their way of life and resources (their tribe). So if "moderates" would disallow killing for beliefs in imaginary things, where would you draw the line, as to when Moontanman's social animal kills appropriately to protect his clan against outsiders? How do you bring the entire world together under one "thought", without the use of adherence to an unquestioned ideal? Iggy, I liked your poem. Regards, TAR2 And in the context of "social animals" consider that conflicts are often settled "man to man" or tusk to tusk as the case might be. In a bar, a fight is often handled by the bouncer saying "take it outside". It then becomes the problem of the neighbors and the local police. In common practice on this Earth you can always dump you problems outside or consider other people's problems, not your problem. It becomes more difficult to enforce "proper" behaviour when the conflict is outside your borders. Then you have to pick sides. Then like in Syria, you have some states backing the rebels and some backing the King, for no particular "reason", that could be considered "universally" agreed upon. Then you have to wonder if your "ideal" is sound enough to pit the U.S. against the Soviet Union, or whether its best to back off and let the King work out his own problems. The point being, that having an ideal that you cannot trump, or get "outside" of, that is the "last word" on any issue or conflicts, is not a bad card to have in your hand. Especially if everybody else in the world would honor the card.

Split Infinity, Judgement is a two edged sword. You, being in the correct group are of the opinion that the thoughts and ways of the other 5 types are in need of correction. Such is one of the general philosophical issues I have with this thread's tonal title. As if to say there is a group of moderate, intelligent but highly judgemental, "unbias" folk, that have risen above the fray and set the standards for humanity, based on reason and ideals of uninspected origin. The idea of a benevolent dictator is not completely out of the question. That there could be someone, pure of heart, and clear of mind, clever and wise, and able to bring all conflicts to the "correct" resolve. But it would still be a dictator, and people generally like to have some say in the matter. The rule of law, itself, is not something that sprang from chemistry equations, after all. The code of Hammerabl and the rules of the old Testament are deeply set in Western law, philosophy and morality. The "idea" of God, the image of a rule giver and ultimate judge, is not "outside" the fabric of our society. People have been brought up, with this thought, that one is responsible to this greater "feeling", this owner of realiity, that does and will hold us accountable for our actions, regardless of what any other man or woman might think of us. As if we get a grade, or will be able to enjoy the fruits of a "good" life...afterward. I am trying to take a logical look at this, as to WHY we have a conscience, and feel its better to help than to hurt. It is almost as if we all are aware of the same thing, and in possession of the same underlying rules and criteria, with which we can judge each other. I am not thinking that this underpinning is automatic. I am thinking that we learn this. The way to be, that is. The way that works the best, for us. The things we are allowed ot be selfish and personally biased about, and the things we must sacrifice for the good of others. And in this light, I do not think that belief in God is an automatic recipe for hatred and war and killing. In the whole history of the world, I am thinking that the image of God, has been quite a help. How do you think things would have gone, if everyone was just out for themselves, from the beginning, with no concern for what would be, after they died. The strong would vanquish the weak, and the law would be the law of the wild. Anarchy is probably the "natural" state of affairs that would have been, without the concern for an afterlife. Without the belief in ideals that have no actual existence. Not a one of us, has the ability to judge the situation, indifferently. We can only pretend there is such a view, and that it matters. And this "belief" does not "break" a man. It may well make a "civilized" man. Regards, TAR2

John Cuthber, I was not trying to say that if a lot of people think a thing, its a step forward. I was trying to say that steps forward need to be taken by a somebody...and the stepper thereby becomes the judge of it's forward nature. In the history of the world, it is often that one man's gain is another man's loss. It is "the final scorekeeper" that I was alluding to. That we would imagine there is one, to judge a step forward, in universal terms. Was thinking on the way home today that I am part of the history of life on this planet, a mere 100 or 120 year maximum part of a very long history, with a potentially very long future...even if its just algae an ants that populate the place in the future. And the whole history, taken when its over, is just a flash, in the timeframe of the universe, to say nothing of immense size of the universe, and the potential "other" stories that have been, are or will be unfolding, on every scale, from quark to galactic string and possibly beyond that. But I was thinking, why? Why does it matter to me? How do I have the right to consider some sort of ownership of and belonging to, such a huge undertaking? My intent, in asking how many people need to know a thing, for the thing to matter, was sort of the reverse of how you took it. It was not to suggest that if a billion people believe in Allah, that that makes Allah so. It was more to suggest that if anybody cares about the whole story, it must be us, and this suggests to me that since there is nobody here, but us chickens, we must be the story, and the story teller, and therefore the metaphysicist's voice is as clear and loud and meaningful, as that of a mathematician or scientist or poet, or for that matter, as clear and loud and meaningful as that of a bleating goat, or a cackling chicken. People that believe in God, may be broken, but as we have decided along the way in this thread, it matters greatly what you believe belief in God is, in the first place. My question was meant to ask, is there "something" that matters, more than what a zillion people know? Split Infinity, Along the lines of your post, in relation to the 6 "types" of people. Is there a way to look at things, from "above" all six? That is, can any type score the other 5 on an unbiased scale and call the sixth the "right way" to look at it? I am thinking that this "seventh" view, is "God's" pervue. Not that there is such an fellow, but that there is such a view, we take, from time to time. Whether we take it literally or figuratively, or both, is a matter of definition, and its difficult to tell someone they cannot actually care about the rest of the universe for any valid reason, when it seems that everybody does, in one way, or another. Regards, TAR2 We are laying to rest the sister of my wife's mother this weekend. As that generation of my wife's family dies, it becomes my wife's generation that holds the "older" generation spot. We become the group, to whom things matter...the judges and the teachers and the holders of the flame of purpose and propriety. Heard a nice saying once. "To the whole world, you are just someone, but to someone, you may be the whole world."

John Cuthber, You bring up a good point. How many people need to be enlightened on a subject, inorder for it to be worthwhile, or a step forward. There are many insights I have had along the way, in 59 years, that were a step forward for me, that were very much like me talking to myself, with nobody else listening. The idea, with only one holder. If one were to imagine something mattering anyway, to the greater reality, in the face of mortality, and solitude, this would not be unlike a belief in God. That one is obligated to reality, somehow completely in its possession and responsible for it. The one who speaks and the one who listens. The one who it matters to, and the one that matters. How may people need to hear a thing, or say a thing, in order for it to be considered a step forward? Why should seeing my wife give birth to my daughter be such a wonderful thing, and such a huge step forward, when such a thing has already been done billions of times, and too many of these wonderful steps forward will overpopulate the Earth and cause its ruin? I am thinking that a metaphysicist commenting in the woods, with nobody to hear her, is a good step forward for the metaphysicist. And if this is true, and it matters to anybody, other than the metaphysicist, then the metaphysicist is not alone, even if there was no other human alive but the fetus in her womb. If we care what others think, and we care about the environment, and we consider the lessons dead people have left for us to learn, and we care about the yet to be born, and arranging things to be of benefit for them, then there is something we care about, that need not hear our voice, inorder to care about our comment. Regards, TAR2

Ok wrong thrice.

Major apology in order. Every time I mentioned the word dudecahedron I was thinking about the The Cube Octahedron. I was never speaking about the dudecahedron. I have an explanation, in that I also have some dudecahedrons lying about, and it is a figure that I "discovered" in drawing on a sphere and trying to determine the "equal" spaces that surround a point, and I simply called the one thing the other, but I have no excuse. It was just a gross, misdirecting, incorrect, mistake. Please accept my apology and replace any instance of "dudecahedron" with "the cube octahedron", in the above thread. Regards, TAR2

Spartian Monkey, I'll go along with the others that have pointed out that God cannot be both dead, AND f**king with us. I'm thinking that a good analogy to the "problem" would be the consideration of the fact that most everybody lacks a full contigent of 8 great grandparents. And I doubt highly that anybody has a full contingent of 16 living great great grandparents. In other words, our creators ARE dead. But that does not mean we do not carry something of them along. When you divide the machine into hardware and software, it is similar to dividing it into material and form. The material alone, does not make the machine, as its the particular form that can carry out the functioning, and the function is not in and of itself material in nature. Soul has more to do with purpose, and form, particular patterns and identities, that identify a lump of matter, as a specific thing with characteristics of its own. If the universe would contain a singular identity, it would by definition have to include every piece and part, characteristic and attribute possible for a universe to have. It would, as a signular thing, not have the ability to be other than itself. In this sense, if God were to be considered the "soul" of the universe, God could not die, without the universe ceasing to be. So that rules out God being dead. So if there is something you have, that your great grandparents had, that you consider a soul, this "identity" has managed to not die, when your great grandparents died. So, whatever piece and part of the identity of the universe that you and I carry, that we consider to be more than just the chemicals that make us up, is as real as the chemicals that make us up. Since we recognize each other as containing this same type of soul thing, its sort of like the universe recognizing itself in the other. AI having a soul is probably not something that will happen when we humans decide a machine has it. It will probably happen, the first time a machine recognizes itself in a human. Regards, TAR2 P.S. I also agree with other posters on this thread, that a "more advanced" race, does not do the trick, as our creator. They themselves would have to have recognized themselves as universe material with an identity other than other universe material, in the first place...and would have the exact same conundrum as we do. Where did that spirit, soul, consciousness, recognition of oneself come from, if there is no place but here (this universe) for it to have come from?

John Cuthber, Well I am tending to agree with you. The octahedral plan uses three axis to locate the place the ray will intersect which triangular face, so I suppose its sort of after the fact, to call that ray a singular direction. Well it is, but you have to use three others to define it, so I've failed there. The movment along an axes however, and then taking one of the 12 directions from there, I have not been able to rule completely out yet. Question. What rules that out? Regards, TAR2

John, Well redundant in that you know they have to add to 60, but not redundant in naming b as the other axis involved, and in giving you the visual that you are 59 degrees from B and one degree from A, in positioning your ray. The triangular funnels seemed doable in this fashion, as in the ternary scheme you linked. But the square funnel seemed more unfriendly to triangulation, and seemed to me to add a flexibility that did not "force" a ray to be in an exact position. Sort of why a triangle is a strong structural shape, where a square can fold up, with two corners going out and two corners coming in. Nothing to insure the corners remained at 90 degrees. But I've dropped that scheme, as being sufficient to name a point with two parameters. However, I had a thought about 45minutes ago, that I would like to explore with you guys and gals that just might still work. One of the aspects of considering the matrix of hexagonal and square planes one can imaginarily build off the figure I pictured, is that each ping pong ball, is a possible "origin" that has the same exact twelve directions as any other pingpong ball in the matrix. Now, let's say our convention was that your first parameter was one of the twelve directions, combined with a number. Say F5.985,940.84757. This first part of the convention would mean travel out in the F direction 5,985,940.84757 units. This position you would be at at this point then becomes the center of a ping ball in a new matrix, that is shifted .84757 units out along the F ray, but in all other regards is oriented in the same directional sense as the first matrix. We then describe our second parameter FROM THERE. Say B598,822.3. F5.985,940.84757 meters , B598,822.3 meters, describes a particular point in space. Any resolution you desire can be used. Only thing left is to mathematically prove that given only the twelve singular directional rays sweeping through space along one ray will completely blanket space. For visual reference, consider a ball with six lethal rods thru it in the agreed upon pattern going off in the twelve directions, as far as the eye can see, floating 100 yards from you. One of the rods is a track that the ball will take in one direction or the other, and the other 5 (10) rods are fixed to the ball. You do not know which of the 6 axis is the track and which of the other 10 rods are fixed, but you know the ball is going to move along the track rod in 1minute in one of the twelve directions at 40000 miles an hour. Is there a position you can take where you know you will not be killed? Regards, TAR2 In motion, in a singular direction, an axis becomes a plane. I am thinking that not only might you be able to name every point in space with this new scheme, but you might be able to name each point in space several different names. Additionally, back to the ternary scheme, and the octahedron. Name the six points of the octahedron A, B, C, D, E, F (as in X, Y, Z, -X. -Y, -Z) and you have the eight triangles XYZ, XY-Z, -XY-Z, -XYZ, X-YZ, X-Y-Z, -X-Y-Z, and -X-YZ. Or naming Y as A, Z as B, X as C, -Y as D, -Z as E, -X as F, you have the more positively named octahedral faces, CAB, CAE, FAE, FAB, CDB, CDE, FDE and FDB, naming the eight general directions, that describe every possible direction, in that every possible ray from the origin, or the center of the octahedron, will either pass thru one of the octahedral faces, or pass thru an edge between two faces or pass thru a point where three faces meet. And thusly be namable as in C20A44B36, C64A36, and C. Thusly naming each direction by the percentage in the ternary schemes 100% total, we have a name for every direction possible and we don't need to travel up a certain amount and over a certian amount and forward a certain amount. We can just make one trip in one direction, and get to any point in the universe, near or far. Only thing left to do is decide what distant quasar is in the A direction.

Iggy, Agreed. Regards, TAR

John Cuthber and Iggy, OK, I thought all day, without coming up with the impossible plan. But I am not ready to throw in the towel yet. As michel123456 suggests, it may be a matter of convention and agreement. Let's say for instance we were to agree only on the fact that no more than twelve same size balls can fit, in the space around a ball.(touching the center ball) And they can be so arranged as in the fashion described in the pictures and diagrams in this thread. That this arrangement is real, exact, reproducable by anyone, anywhere, and would be true, and the same figure with the same relationships, anywhere it was constructed, on any scale it would be contructed and would stay the same figure under any and all rotations, with the infinite amount of rays emminating outward only, from the center of the center ball, passing through every concievable point in space. Then we agree that one of these infinite number of rays passes through the center of ball A and continues outward in that direction infinitely, passing through every point that lies exactly in that direction. We call that direction A. We do the same for ball B, and call that ray, direction B. We then consider the infinite amount of rays in the fan of rays that lie between A and B, and give them each a name by a regular and descriptive convention, let's say for instance 59A1B would be that unique ray that went outward one degree away from A and 59 degrees away from B. This would give us a name for that ray, with no reference to any inclination, plane, altitude. There is only one percise and distinct direction defined by 59A1B. Under this convention we might also call direction A, by another name 60A0B Thusly proceeding we could name every ray in the fan between A and B, the fan between B and C and the fan between C and A. And we have those directions named. Then someone more mathematically clever than I comes up with the extension of the convention to include the rays inside the triangle funnel. What would the ray in the middle of the three, be named? Does 30A30B30C work out? If so, then we could name every possible ray within the triangular funnel passing thru that face of the dudecahedron. Then the task is to figure the convention for the square funnel bounded by the 60 degree fans AB, BL, LK and KA, a little more challenging but probably mathematically possible. The BK fan is 90 degrees worth of rays, as is the AL fan. If the conventions were agreed on, we could drop the lattice and balls and just consider that any point in space must in the singular direction of one and only one of the named rays. Regards, TAR2 Infinite precision can be achieved by decimal degrees, or minutes and seconds or whatever. P.S. But alas you could probably do the same thing with an octahedron. Consider each equilateral triangle, dropped into xyz funnel, normal to the origin, and name your rays through it. I don't know if that means you can name a direction and a distance and define a point, or whether it just means you need at least three and no more than three dimensions to define a point. Well yes I do know. It's the latter. In the words of John Cuthber, "Its not a debate, its a fact." I yield.

John Cuthber, Conventionally speaking, I have no argument. But even though the system is not well defined, nor agreed upon, just by looking at my diagram, you know what direction I mean by J, and no latitude or longitude, left or right, hieght or width, altitude, or declination was mentioned. You can simply go in J. Regards, TAR

John Cuthber, Come to think of it, there is no particular reason to have 3 positive directions, and 3 negative ones, as desribed in Cartesian Coordinates. From an origin, any direction you go is still "away", and in this sense a positive accrual.<br /><br />To get to a point in Cartesian coordinates you have to make three trips in positive or negative directions each parallel to one of the axes.<br /><br />With a directional parameter, you just go a prescribed distance in the one positive direction mentioned.<br /><br />Go 3 in J.<br /><br />Regards, TAR2

Iggy, Was fun for me to have descovered the figure and the dense pack arrangement on my own, a number of years ago, and then find it had a name and studied attributes. Nothing new, under the sun, but discovery is fun, anyway. The sphere I am envisioning we can imagine ourselves within, is the central ping pong ball. Have not yet determined the nature of the longitudinal lines, but I am thinking it will not have any latitudinal lines, just longitudinal with 12 poles, perhaps. Or four equators on the hexagonal planes and three on the square planes? Regards, TAR2 John Cuthber, I understand what you are saying, but is NNW any less or more one direction as NNNW? Under the circumstances, a decimal or fractionin a distance is introducing the same kind of complexity. Bisecting an angle, so to speak. The key here, or the question here, is can we come up with a way to divide direction in a natural and regular, and predictable and precise way. If so, it can be one parameter, infinitely divisible along the agreed upon plan. Regards, TAR2

org8bearded1, The latitude and longitude lines are a little contrived, in a sense. The latitude lines circles on the sphere, of different circumferences and the longitude lines circles that intersect, for no particular reason at only two points, a North and a South Pole. The two seem to be delinating two different things, not of the same size and characteristics. Somewhat like a failed attempt to put a 90degree grid on a sphere. At the North pole, one step can take you across longitude lines that would take you hundreds of thousands of steps to cross. On the other hand the sphere is rather friendly to angles described by the dense packing of spheres in the intersecting hexagonal pattern embedded in the dudecahedron. The 3d square coordinates are visible, but those pesky corners are cut off, making it easier to see how space fits around a point. In a cube setup, you go in 6 directions in whole numbers and have to go in the other direction in square roots and combinations of square roots and pi and such. In the hexagonal, you can go whole number out, in 12 different directions. In all directions, so to speak. You still have to do math to go between the axes, but its the same math (though I don't know what that would be, yet). Its triangular 60degree math of some sort. Regards, TAR2 Diagram titles include "cut the corners off a cube", "draw lines between opposing faces", "small marker balls", and "small marker balls, lettered". The six purple axes define the twelve directions I am talking about. The 7 multicolored lines connect the center of the faces of the dudecahedron, tying the system to xyz coordinates. The marker balls are located at the corners of the dudecahedron. Their relative positions are the exact position twelve larger balls would take, if fit around a central ball of the same size, in the four intersecting hexagonal plane pattern described. (drawing full size balls that did not obscure one another in a two dimensional rendering was beyond my "paint" skills.)

Iggy, Well I suppose I am after a way to define a direction (from an origin) in space with one parameter. Points themselves take up no space at all. Being such, you can not fill space with points. Perhaps the lattice built out from a central sphere is not bounding 40% of space, but any arrangement of points you design is bounding exactly none of space. At least a sphere is real, bounding a particular amount of space, and dense packed spheres fit space, and say something about it, in terms of what it is, and is not. At least to me. As to what the math would be like in such a system, I have not come close to figuring out. I have enough trouble trying to figure out even the angles involved, between the intersecting planes. I do not know how to work with solid angles. Its perplexing enough for me that I can draw 90 degree angles on a ping pong ball making a three sided figure. But, if you would want to set equally spaced rays out from the Cartesian Origin so to define equal and divisible amounts of direction, it is difficult. You know you must have one eighth of direction in each of the volumes bounded by the planes of the axes, but not easy to see how to divide that amount of direction up into equal parts. If you could divide a quadrant up into eight equal parts, all of the same shape, and then each of them into eight parts of equal parts and so on, each "volume" touching the origin, you could use a base eight number with an octal point, to give a number to a direction. Seems like the area your rays would describe on the surface of a unit sphere centered on the origin would be the best way to determine if your rays were defining equal amounts of direction. In anycase the math gets to complicated for me, to be taking all the squareroots and do all the sine cosine stuff. keeping the "square" space of xyz coordinates in mind. Its easier for me to just see how the ping pongs balls actually fit into space. Making me think, that when it comes to numbering direction, the six axes system might be more suited for the job, than the three axes one. Regards, TAR2

So if we would have to be assuming some parameters to spiral out our point size, it would probably be best to assume something actual. That is, take something from nature and or ping pong balls as to how an entity actually fits into space. What are the parameters which which it HAS to operate. The spiraling cubes leave me with the question of how to fill space in a regular pattern, that winds up covering up, down, left, right, foward and back. There may be a clue in a dodechahedra in that one can form such, by cutting the corners off a cube to the midpoint of the edges of the cube. Leaving one with a 14 sided figure, 8 equal length triangles, and 6 diamonds or squares each of them with edges of the same lengths as the triangle's edges. Dense packing ping pong balls around a central ping pong ball, winds you up with the same shape, with the center of each of the surrounding ping pong balls, on each of the corner points of the dodecahedron. And you have described the six axes all regularly angled from the others, and have positioned the intersecting hexagonal and square planes required to "fill" space in all directions, in a regular, whole number (sphere diameter) manner. Perhaps the spiraling out function would be something similar to a three dimensional fractal pattern. Or somehow Fibonocci would come into play, but I would rather find the answer in the way that things actually fit into space, than to assume a thing and impose it. Sorry Iggy, We cross posted. I will submit that I am working with a lattice, and I will also submit to the success of the work others have done to form the coordinate systems that we use. Though I will retain the right to call any explanation or description we come up with, human friendly, of human origin and utility and understandable in a human fashion. Besides you can't say that 3D is simply the way it is, when we simultaneously decided that it takes at least four to describe it. The cartesian system is a lattice of sorts, with each one dimensional point on the corner of a unit cube, with each edge divisible and the diagonal between corners figurable with sines and cosines, tangents and the like. The sphere is assumed or emerges from the plan. Why not start with the matrix of spheres and let the triangles and cubes emerge from that? Regards, TAR2

Iggy, Well, I agree with the others too. I have been working this problem for years and always have come to that same conclusion, that its redundant to use 6 axis to do the job that 3 will do...except I had a glimmer the other night, that escapes me now, and I am working at recapturing it. Hence the thread. While I understand the three degrees of freedom, they have something to do with how we think and see things. Things infront and behind. Things up and down. And things left and right. Seems to me, that to understand Cartesian coordinates you need to be standing at the origin with y above you, negative y below you, negative x to your left, positive x to your right, z in front of you, and negative z behind. Since you have to be standing, and have two hands and a face to concieve of this coordinate system, and we all have such equipment, it works fine, and is quite readily taught and has become the standard and is popular. However its quite anthropomorphic. Not that that is bad, we have no other starting point to start from but our own here, but that in playing with the ping pong balls and the dodecahedra its occured to me, that space is more like the dodecahedra in structure than a cube...hence my quest. There are more spheres floating and bouncing around the place at all grain sizes, than cubes. Perhaps there would be reason to grasp the concept of 6 axis. Building out the dodecahedron intersecting planes become evident. Four hexagonal(or triangular) planes, and three square planes...its really quite intriging...and speaks of a "regular" and symetrical space made of angles and relationships, not humanly intuitive or readily concieved of in cartisian coordinates, but simple and real and satisfying, none-the-less. If each of these 12 directions is a repeating pattern and we would know what the pattern looked like, if we were facing it, and we could decribe with a number every singular aspect or "direction" possible in that direction. Since we can pick H as the 1/12 of direction we are facing, then the puzzle would be down to describing the possible direction aspects within this view with a number or symbol system. Then H 4958B.34A01(base12) would be a unique and singular direction, one parameter. And with a distance parameter, two parameters could describe any point in space, from your origin. Regards, TAR2

John Cuthber, Well there are "gaps" between points on a line as well. We seem to overcome that with decimals. Choice of units or sphere size could get you at least to within an atom's reach of a point. Which would be useful in most situations. I did not nail down the concept yet, and am a bit slowed down by having to come up with a way to define an infinite amount of directions with one parameter, but it does not seem "impossible" to me. In playing with ping pong balls in a dense pack pattern, the collection seems to show aspects of space, nicely, in whole number increments, and reveal relationships that are not so whole number understandable as when space is defined in cartesian coordinates, with various whole number ray lengths from the origin defined by the combination of three decimals. Would be my goal to simply define the direction, once. And then simply define the distance once. Regards, TAR2