1) Offset positive a negative (yes/no) states. Presumably these come from the idea that the "maybe" state from which the algorithm takes its form allows for both, although only the algorithm itself requires both.
2) Off set angles converging of pi
3) Information quantities diverging as an F-series or as this
4) Compression states converging as an F-series F(n)^(2^n) as in increases one unit at a time.
Another novelty of F series is that if you subtract one from the prior, offset by one, of necessity you get another F-series of numbers. In this way, we have, with offset intersecting spirals a solution which is one F-series and slightly off angularly from the prior one which is the solution observed.
The reflection of compression comes in many fashions showing we are moving towards a compressive state. What we call an information revolution is an example. In this case, information is compressed to reflect our movement towards a more organized compressed state from a less compressed one at least locally. Eventually, we will move to decompression and this information will all disappear.
Another place is the concentration of people in cities. These are aspects of civilization but they are also aspects of compression.
These all relate to a common point of origin, but you have the true F-series (1,1,2,3,5) and the modified F-series for all the information in the universe F(n)=(n+(n-1)+(n-2)) which shows that the current total amount of information is basedd on all the information in all the histories of the universe.
One question which remains is whether F(n) ends here or whether it includes n-3 and beyond except they are too small to affect the solution substantially.
That is for another day, however.
Anyway, enough work, time for something a little more entertaining
I'm rewriting Socrates to be novella length-here is an insert from the rewrite
Parminides finished the walk to the wall gates of the Palace di Novo and shuffled up to the guards who looked at the dusty figure asking for Governor Pulicus with great suspicion. He did not look like an assassin, but protecting the governor from senile old men was also within their authority.
Parminides merely anounced himself and then sat on a concrete table meant for some uncarved statue and rested his feet. The guard who was questioning him called for a young boy who was inside the walls and sent him running. You never knew with the governor's moods what spontaneous whim he might pursue, perhaps his new passion was interviewing old men.
The boy returned, and spoke to the guard, not even a little windedd and Parminides grumbled to himself of lost youth and the waste of giving it to this small boy with nothing more important to do than run errands for guards. The guards did nothing, but seemed all the more suspicious of Parminides for all of that. He would have left but his feet hurt and the statuary stand was as comfortable as anywhere else in the shade of the towering walls.
After a few minutes another boy came and talked to the first briefly and then to the guards who now straightened up. Soon a small entourage of well dressed bearded men in their prime came through the door and divided to show a middle aged but powerful man with a neatly trimmed beard. "Parminides! You walked. If you had asked I would have sent a chariot for you."
"If you had sent the offer, I would have accepted." The guards now stood at attention, showing more attention to this man who spoke so casually, almost insultingly to the governor who held life and death in his hands.
"Come walk with us," Publicus said giving a gesture that caused the others to drop behind the. Parminides decided against giving him the satisfaction of admitting his exhaustion after the long trip and the walk to the palace.
"Do you wish to talk of the trial?" Publicus asked.
"I do not."
"This way," Publicus said and they entered a garden. "There are over a hundred acres enclosed within the palace grounds, the hills provide a natural barrier and the stream you see winds through." There were trees on either side of the bubbling brook which made pleasant sounds and the water seemed to cool the air greatly.
"I remember," Publicus continued, "that you loved to lecture when you were younger. You seem to be quieter in your old age."
Parminides stubbed his toe on a rock and skipped for a second. When he caught his balance he had time to respond, "I have been working through a problem in my mind, it has worried me."
"But not your trial. You disappoint me in what you see as important. I like that young fellow Zeno, but he will get you in trouble. If you were willing to sacrifice that young man your problems would go away."
Parminides said nothing, just signed in concert with the brook.
"There are fish in the deeper pools. They are delicious. I know you are a learned man and your teachings when I was a young man were invaluable to me."
"I never taught you to kill men, someone else seems to have taught you better than me."
"But you taught me how to calculate how much food men would need, how much a city needs to withstand a seige or to live well. Those are skills of a general and a governor."
"So my time was not wasted."
"Don't condescend to me."
"You summoned me here. Did you do so out of nostalgia?"
"I was hoping for some new counsel, some new insight."
"Older men have to ask question to find answers, only children don't know what questions to ask."
"I am not a child but I will not let you antagonize me. You seemed difficult to me then, I thought it was a child's eyes. Do you remember striking my hand with a stick?" Parminides nodded, thinking of the child from so long ago that had been so hard to keep focused. He wondered if his old student would have him beat with a stick. Publicus was a fierce man, huge biceps, not as tall as parminides, but more commanding, the strides of a man in his prime who hadd lded armies and might lead them again.
"I am one of the most powerful men in the most powerful country in the world, my power stretches farther than a man or horseback can travel in a week. There are semafores but it takes a week for any information of consequence to reach me from the borders. If I go to the borders, I can see my enemies not 5 minutes by a fast walk, and yet I cannot touch the, I can cause them no harm, my reach is restricted."
"I am sorry you are not able to kill faster," Parminides answered.
"Perhaps I should have guessed you would not be sympathetic to the needs of a ruler." They came upon a small alter. "Do you hunt? Perhaps we could kill something for a sacrifice? No? Your friend Zeno loves to hunt. But no, I can see you have lost your interest."
"I mostly eat green things, I have become a cow in my old age."
"I hate the priests myself. But their churches bring jobs to a town that otherwise would have none. The sacrifces feed the poor andd it brings comfort. Can you tell me how to find comfort from the priests?"
"I lost my faith. The stories of the ancient heros are children's tales."
"You made me memorize them."
"I tried and failed. But the exercise of trying perhaps helped you."
" The stories of Hercules are monster stories. I think perhaps they would have been more interesting had the monsters won more often."
"You are right." Parminides thought of this interpretation andd saw the brightness he had seen in his old studdent. He wondereed to himself what Publicus really wanted. He could not expect that Parminides was hiding some secret to the problems he had mentioned.
"They would be more interesting if there were still monsters."
There are many monsters still left, otherwise you would not have walls and armies." Now Publicus was quiet.
"I do not deal with practical problems."
"Then tell me what you do deal with these days?"
"There are logical problems with space that bother me."
"I have heardd Zeno try to explain this." Parminides was surprised and his look must have shown it because Publicus added, "I do not live within these walls all of the time and Zeno is entertaining. Tell me about space an why an arrow will not strike you deadd if it only travels half way to you?"
"That is a child's explanation. The problem is more complex than describing the arrow, the problem is describing why an arrow exists at all, why it is there to be fired why we know it was fired."
"You see," Parminides was lecturing as they walked, more to fill the time till Publicus was ready to speak and partially because this was the problem that he hadd worried over, "things ha to start from some logical point or we would not have logic which must reflect this beginning. So we start from zero andd build outward, but there is some mathematical formula that should cover this building.
"I believe there must be some place from which postive things and negative things come, but in some way that the positive over times comes to overwhelm an equal amount of negative, as if they both change together, but some formula shows an exponentially greater growth at each change for the positive with the negative following a step behind. In this way, we see the positive and the negative, but the postive seems to overwhelm the negative."
[editor's note]Parminides saw, but could not explain the effect of f-series expansion which is that differences are multiplied due to exponential length changes which is why we see so much more of positive spiral. At the time of expansion, there seems to be nothing more than pockets of negative, but what would be seen at the point of net compression?
"I believe the steps must be discrete, that the past is somehow incorporated into these discrete steps so that we see history because it is built into the present. But somehow, the steps of the equal size must appear different and change with time."
"I cannot always see what is written for me," Publicus tells him.
Ah, the problem at last. "When you hold it far from your face, it becomes more clear?" Parminides asks, dropping his train of thought for this more immediate problem.
"Yes. It is a weakness, I cannot have weakness of this type."
"And yet you do. It means you will be able to see your enemies from a great distance for many years. It is a blessing. I can no longer see what is far away. Our strengths balance our weaknesses."
"I do not need your platitudes. you have no solution?"
"A curved pool in a clear container will make the words appear bigger underneath, polished shells till they are paper thin. When not around a reader who you trust to read accurately."
"Yourself?"
"I am too old to keep up with you. I could find someone."
"Zeno?" It is almost snorted with derision.
"Zeno would make up what he things the message should say. I can find someone, I think, smart with no ambition."
"You want me to solve your problems in return?"
"I am tired. I feel alone even when I am with others. I worry constantly. What would you do to help someone who would kill himself if he were not too afraid?"
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